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diff --git a/src/interp/nag-d02.boot.pamphlet b/src/interp/nag-d02.boot.pamphlet new file mode 100644 index 00000000..93edfc46 --- /dev/null +++ b/src/interp/nag-d02.boot.pamphlet @@ -0,0 +1,2168 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/interp nag-d02.boot} +\author{The Axiom Team} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\section{License} +<<license>>= +-- Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd. +-- All rights reserved. +-- +-- Redistribution and use in source and binary forms, with or without +-- modification, are permitted provided that the following conditions are +-- met: +-- +-- - Redistributions of source code must retain the above copyright +-- notice, this list of conditions and the following disclaimer. +-- +-- - Redistributions in binary form must reproduce the above copyright +-- notice, this list of conditions and the following disclaimer in +-- the documentation and/or other materials provided with the +-- distribution. +-- +-- - Neither the name of The Numerical ALgorithms Group Ltd. nor the +-- names of its contributors may be used to endorse or promote products +-- derived from this software without specific prior written permission. +-- +-- THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS +-- IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED +-- TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A +-- PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER +-- OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, +-- EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, +-- PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR +-- PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF +-- LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING +-- NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS +-- SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + +@ +<<*>>= +<<license>> + +d02bbf() == + htInitPage('"D02BBF - ODEs, IVP, Runge-Kutta-Merson method, over a range, intermediate output",nil) + htMakePage '( + (domainConditions + (isDomain PI (PositiveInteger))) + (text . "\windowlink{Manual Page}{manpageXXd02bbf} for this routine ") + (text . "\newline ") + (text . "\lispwindowlink{Browser operation page}{(|oPageFrom| '|d02bbf| '|NagOrdinaryDifferentialEquationsPackage|)} for this routine") + (text . "\newline \horizontalline ") + (text . "\newline ") + (text . "D02BBF integrates a system of {\it n} ordinary differential ") + (text . "equations, {\htbitmap{yi}}' = {\htbitmap{fi}}(x,y), for ") + (text . "{\it i} = 1,2,...,{\it n}, over a range with given initial ") + (text . "conditions using a Runge-Kutta-Merson method; the solution ") + (text . "may be output at specified points.") + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Initial value of {\it x}:") + (text . "\newline\tab{2} ") + (bcStrings (5 "0.0" x F)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "End of integration range {\it xend}:") + (text . "\newline\tab{2} ") + (bcStrings (5 "8.0" xend F)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Number of differential equations {\it n}:") + (text . "\newline\tab{2} ") + (bcStrings (5 3 n PI)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "\newline Tolerance required {\it tol}: ") + (text . "\newline\tab{2} ") + (bcStrings (10 "0.0001" tol F)) + (text . "\blankline ") + (text . "\newline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Error control indicator {\it irelab}:") + (radioButtons irelab + ("" " 0, mixed" mix) + ("" " 1, absolute" abs) + ("" " 2, relative" rel)) + (text . "\blankline ") + (text . "\newline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Ifail value:") + (radioButtons ifail + ("" " -1, Print error messages" minusOne) + ("" " 1, Suppress error messages" one))) + htMakeDoneButton('"Continue", 'd02bbfSolve) + htShowPage() + +d02bbfSolve htPage == + x := htpLabelInputString(htPage,'x) + xend := htpLabelInputString(htPage,'xend) + n := + $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'n) + objValUnwrap htpLabelSpadValue(htPage, 'n) + tol := htpLabelInputString(htPage,'tol) + control := htpButtonValue(htPage,'irelab) + irelab := + control = 'mix => '0 + control = 'abs => '1 + '2 + error := htpButtonValue(htPage,'ifail) + ifail := + error = 'minusOne => '-1 + '1 + n = '3 => d02bbfDefaultSolve(htPage,x,xend,tol,irelab,ifail) + funcList := + "append"/[fa(i) for i in 1..n] where fa(i) == + prefix := ('"\newline {\em Function ") + prefix := STRCONC(prefix,STRINGIMAGE i,'":} \space{1}") + funct := STRCONC ('"Y[",STRINGIMAGE i ,"]") + nam := INTERN STRCONC ('"n",STRINGIMAGE i) + [['text,:prefix],['bcStrings,[42, funct, nam, 'EM]]] + middle := ('"\blankline \menuitemstyle{} \tab{2} Enter the initial ") + middle := STRCONC(middle,'"values of \htbitmap{yi}: \newline \tab{2}") + yList := + "append"/[fb(i) for i in 1..n] where fb(i) == + ynam := INTERN STRCONC ('"u",STRINGIMAGE i) + [['bcStrings,[6, 0, ynam, 'F]]] + yList := [['text,:middle],:yList] + mid:= ('"\blankline \menuitemstyle{} \tab{2} Intermediate values of {\it x}") + mid := STRCONC(mid,'" at which \htbitmap{yi} is required: \newline \tab{2}") + vList := [['bcStrings,[30, "0", 'out, 'EM]]] + vList := [['text,:mid],:vList] + equationPart := [ + '(domainConditions + (isDomain EM $EmptyMode) + (isDomain S (String)) + (isDomain F (Float)) + (isDomain I (Integer))), + :funcList,:yList,:vList] + page := htInitPage('"D02BBF - ODEs, IVP, Runge-Kutta-Merson method, over a range, intermediate output",nil) + htSay '"\menuitemstyle{}\tab{2} " + htSay '"Enter the functions (i.e. the derivatives) below " + htSay '"as functions of Y[1]...Y[n]: " + htSay '"\newline " + htMakePage equationPart + htMakeDoneButton('"Continue",'d02bbfGen) + htpSetProperty(page,'x,x) + htpSetProperty(page,'xend,xend) + htpSetProperty(page,'n,n) + htpSetProperty(page,'tol,tol) + htpSetProperty(page,'irelab,irelab) + htpSetProperty(page,'ifail,ifail) + htpSetProperty(page,'inputArea, htpInputAreaAlist htPage) + htShowPage() + +d02bbfDefaultSolve(htPage,x,xend,tol,irelab,ifail) == + n := '3 + page := htInitPage('"D02BBF - ODEs, IVP, Runge-Kutta-Merson method, over a range, intermediate output",nil) + htMakePage '( + (domainConditions + (isDomain EM $EmptyMode) + (isDomain F (Float)) + (isDomain I (Integer))) + (text . "\newline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Enter the functions (i.e. the derivatives) below ") + (text . "as functions of Y[1]...Y[n]: ") + (text . "\newline ") + (text . "\newline {\em Function 1:} \space{1}") + (bcStrings (44 "tan(Y[3])" f1 EM)) + (text . "\newline {\em Function 2:} \space{1}") + (bcStrings (44 "-0.032*tan(Y[3])/Y[2] -0.02*Y[2]/cos(Y[3])" f2 EM)) + (text . "\newline {\em Function 3:} \space{1}") + (bcStrings (44 "-0.032/(Y[2]**2)" f3 EM)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Enter the initial values of \htbitmap{yi}:") + (text . "\newline \tab{2}") + (bcStrings (8 "0.0" y1 EM)) + (bcStrings (8 "0.5" y2 EM)) + (bcStrings (8 "\%pi*0.2" y3 EM)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Intermediate values of {\it x} at which \htbitmap{yi} is required:") + (text . "\newline \tab{2}") + (bcStrings (30 "1,2,3,4,5,6,7,8" out EM))) + htpSetProperty(page,'x,x) + htpSetProperty(page,'xend,xend) + htpSetProperty(page,'n,n) + htpSetProperty(page,'tol,tol) + htpSetProperty(page,'irelab,irelab) + htpSetProperty(page,'ifail,ifail) + htMakeDoneButton('"Continue",'d02bbfGen) + htpSetProperty(page,'inputArea, htpInputAreaAlist htPage) + htShowPage() + +d02bbfGen htPage == + x := htpProperty(htPage, 'x) + xend := htpProperty(htPage, 'xend) + n := htpProperty(htPage, 'n) + tol := htpProperty(htPage, 'tol) + irelab := htpProperty(htPage, 'irelab) + ifail := htpProperty(htPage, 'ifail) + alist := htpInputAreaAlist htPage + y := alist + outp := ((first y).1) + oList := [outp,:oList] + y := rest y + ostring := bcwords2liststring oList + -- This is distictly horrible! OUTP is a comma-seperated string so we + -- count up the commas to see how many elements it has. We return this + -- quantity plus 1 since the ASP OUTPUT is always called at least once. + numberOfPoints := + ZEROP LENGTH(outp) => 1 + 2+COUNT(CHARACTER(44),outp) + for i in 1..n repeat + ytemp := STRCONC((first y).1," ") + yList := [ytemp,:yList] + y := rest y + ystring := bcwords2liststring yList + while y repeat + f := STRCONC((first y).1," ") + fList := [f,:fList] + y := rest y + fstring := bcwords2liststring fList + prefix := STRCONC("d02bbf(", xend,", ", STRINGIMAGE numberOfPoints, ", ",STRINGIMAGE n,", ",STRINGIMAGE irelab) + prefix := STRCONC(prefix,", ",x,", [", ystring,"],",tol) + prefix := STRCONC(prefix,", ",STRINGIMAGE ifail,",(") + end := STRCONC(fstring,"::Vector Expression Float)::ASP7('FCN),(",ostring) + end := STRCONC(end,"::Vector MachineFloat)::ASP8('OUTPUT))") + linkGen STRCONC(prefix,end) + +d02bhf() == + htInitPage('"D02BHF - ODEs, IVP, Runge-Kutta-Merson method, until function of solution is zero",nil) + htMakePage '( + (domainConditions + (isDomain PI (PositiveInteger))) + (text . "\windowlink{Manual Page}{manpageXXd02bhf} for this routine ") + (text . "\newline ") + (text . "\lispwindowlink{Browser operation page}{(|oPageFrom| '|d02bhf| '|NagOrdinaryDifferentialEquationsPackage|)} for this routine") + (text . "\newline \horizontalline ") + (text . "\newline ") + (text . "D02BHF integrates a system of {\it n} ordinary differential ") + (text . "equations, {\htbitmap{yi}}' = {\htbitmap{fi}}(x,y), for ") + (text . "{\it i} = 1,2,...,{\it n}, over a range with given initial ") + (text . "conditions using a Runge-Kutta-Merson method until a specified ") + (text . "function {\em g(x,y)} of the solution is zero. ") + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Initial value of {\it x}:") + (text . "\newline\tab{2} ") + (bcStrings (5 "0.0" x F)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "End of integration range {\it xend}:") + (text . "\newline\tab{2} ") + (bcStrings (5 "10.0" xend F)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Number of differential equations {\it n}:") + (text . "\newline\tab{2} ") + (bcStrings (5 3 n PI)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "\newline Tolerance required {\it tol}: ") + (text . "\newline\tab{2} ") + (bcStrings (10 "0.0001" tol F)) + (text . "\blankline ") + (text . "\newline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Error control indicator {\it irelab}:") + (radioButtons irelab + ("" " 0, mixed" mix) + ("" " 1, absolute" abs) + ("" " 2, relative" rel)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "\newline Upper bound on size of the interval {\it hmax}: ") + (text . "\newline\tab{2} ") + (bcStrings (10 "0.0" hmax F)) + (text . "\blankline ") + (text . "\newline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Ifail value:") + (radioButtons ifail + ("" " -1, Print error messages" minusOne) + ("" " 1, Suppress error messages" one))) + htMakeDoneButton('"Continue", 'd02bhfSolve) + htShowPage() + +d02bhfSolve htPage == + x := htpLabelInputString(htPage,'x) + xend := htpLabelInputString(htPage,'xend) + n := + $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'n) + objValUnwrap htpLabelSpadValue(htPage, 'n) + tol := htpLabelInputString(htPage,'tol) + control := htpButtonValue(htPage,'irelab) + irelab := + control = 'mix => '0 + control = 'abs => '1 + '2 + hmax := htpLabelInputString(htPage,'hmax) + error := htpButtonValue(htPage,'ifail) + ifail := + error = 'one => '1 + '-1 + n = '3 => d02bhfDefaultSolve(htPage,x,xend,tol,irelab,hmax,ifail) + funcList := + "append"/[fa(i) for i in 1..n] where fa(i) == + prefix := ('"\newline {\em Function ") + prefix := STRCONC(prefix,STRINGIMAGE i,'":} \space{1}") + funct := STRCONC ('"Y[",STRINGIMAGE i ,"]") + nam := INTERN STRCONC ('"n",STRINGIMAGE i) + [['text,:prefix],['bcStrings,[42, funct, nam, 'EM]]] + middle := ('"\blankline \menuitemstyle{} \tab{2} Enter the initial ") + middle := STRCONC(middle,'"values of \htbitmap{yi}: \newline ") + yList := + "append"/[fb(i) for i in 1..n] where fb(i) == + ynam := INTERN STRCONC ('"u",STRINGIMAGE i) + [['bcStrings,[6, 0, ynam, 'F]]] + yList := [['text,:middle],:yList] + mid:= ('"\blankline \menuitemstyle{} \tab{2} Enter the function below ") + mid := STRCONC(mid,'"{\em g(x,y)}: \newline ") + vList := [['bcStrings,[30, '"Y[1]", 'g, 'EM]]] + vList := [['text,:mid],:vList] + equationPart := [ + '(domainConditions + (isDomain EM $EmptyMode) + (isDomain S (String)) + (isDomain F (Float)) + (isDomain I (Integer))), + :funcList,:yList,:vList] + page := htInitPage('"D02BHF - ODEs, IVP, Runge-Kutta-Merson method, until function of solution is zero",nil) + htSay '"\menuitemstyle{}\tab{2} " + htSay '"Enter the functions (i.e. the derivatives) below \htbitmap{fi} " + htSay '"as functions of Y[1]...Y[n]: " + htSay '"\newline " + htMakePage equationPart + htMakeDoneButton('"Continue",'d02bhfGen) + htpSetProperty(page,'x,x) + htpSetProperty(page,'xend,xend) + htpSetProperty(page,'n,n) + htpSetProperty(page,'tol,tol) + htpSetProperty(page,'irelab,irelab) + htpSetProperty(page,'hmax,hmax) + htpSetProperty(page,'ifail,ifail) + htpSetProperty(page,'inputArea, htpInputAreaAlist htPage) + htShowPage() + +d02bhfDefaultSolve(htPage,x,xend,tol,irelab,hmax,ifail) == + n := '3 + page := htInitPage('"D02BHF - ODEs, IVP, Runge-Kutta-Merson method, until function of solution is zero",nil) + htMakePage '( + (domainConditions + (isDomain EM $EmptyMode) + (isDomain F (Float)) + (isDomain I (Integer))) + (text . "\newline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Enter the functions (i.e. the derivatives) below \htbitmap{fi} ") + (text . "as functions of Y[1]...Y[n]: ") + (text . "\newline {\em Function 1:} \space{1}") + (bcStrings (44 "tan(Y[3])" f1 EM)) + (text . "\newline {\em Function 2:} \space{1}") + (bcStrings (44 "-0.032*tan(Y[3])/Y[2] -0.02*Y[2]/cos(Y[3])" f2 EM)) + (text . "\newline {\em Function 3:} \space{1}") + (bcStrings (44 "-0.032/(Y[2]**2)" f3 EM)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Enter the initial values of \htbitmap{yi}:") + (text . "\newline ") + (bcStrings (8 "0.5" y1 EM)) + (bcStrings (8 "0.5" y2 EM)) + (bcStrings (8 "\%pi*0.2" y3 EM)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Enter the function below {\em g(x,y)}: ") + (text . "\newline ") + (bcStrings (30 "Y[1]" g EM))) + htpSetProperty(page,'x,x) + htpSetProperty(page,'xend,xend) + htpSetProperty(page,'n,n) + htpSetProperty(page,'tol,tol) + htpSetProperty(page,'irelab,irelab) + htpSetProperty(page,'hmax,hmax) + htpSetProperty(page,'ifail,ifail) + htMakeDoneButton('"Continue",'d02bhfGen) + htpSetProperty(page,'inputArea, htpInputAreaAlist htPage) + htShowPage() + +d02bhfGen htPage == + x := htpProperty(htPage, 'x) + xend := htpProperty(htPage, 'xend) + n := htpProperty(htPage, 'n) + tol := htpProperty(htPage, 'tol) + irelab := htpProperty(htPage, 'irelab) + hmax := htpProperty(htPage, 'hmax) + ifail := htpProperty(htPage, 'ifail) + alist := htpInputAreaAlist htPage + y := alist + g := ((first y).1) + y := rest y + for i in 1..n repeat + ytemp := STRCONC((first y).1," ") + yList := [ytemp,:yList] + y := rest y + ystring := bcwords2liststring yList + while y repeat + f := STRCONC((first y).1," ") + fList := [f,:fList] + y := rest y + fstring := bcwords2liststring fList + prefix := STRCONC("d02bhf(", xend,", ",STRINGIMAGE n,", ",STRINGIMAGE irelab) + mid := STRCONC(", ",hmax,", ",x,", [", ystring,"],") + mid := STRCONC(mid,tol,", ",STRINGIMAGE ifail,",(",g) + mid := STRCONC(mid,"::Expression Float)::ASP9('G),(") + end := STRCONC(fstring,"::Vector Expression Float)::ASP7('FCN))") + linkGen STRCONC(prefix,mid,end) + + +d02cjf() == + htInitPage('"D02CJF - ODEs, IVP, Adams method, until function of solution is zero, intermediate output",nil) + htMakePage '( + (domainConditions + (isDomain PI (PositiveInteger))) + (text . "\windowlink{Manual Page}{manpageXXd02cjf} for this routine ") + (text . "\newline ") + (text . "\lispwindowlink{Browser operation page}{(|oPageFrom| '|d02cjf| '|NagOrdinaryDifferentialEquationsPackage|)} for this routine") + (text . "\newline \horizontalline ") + (text . "\newline ") + (text . "D02CJF integrates a system of {\it n} ordinary differential ") + (text . "equations, {\htbitmap{yi}}' = {\htbitmap{fi}}(x,y), for ") + (text . "{\it i} = 1,2,...,{\it n}, over a range with given initial ") + (text . "conditions using an Adams method until a specified ") + (text . "function {\em g(x,y)} of the solution is zero; the solution may ") + (text . "be output at specified points. \blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Initial value of {\it x}:") + (text . "\newline\tab{2} ") + (bcStrings (5 "0.0" x F)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "End of integration range {\it xend}:") + (text . "\newline\tab{2} ") + (bcStrings (5 "10.0" xend F)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Number of differential equations {\it n}:") + (text . "\newline\tab{2} ") + (bcStrings (5 3 n PI)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "\newline Tolerance required {\it tol}: ") + (text . "\newline\tab{2} ") + (bcStrings (10 "0.0001" tol F)) + (text . "\blankline ") + (text . "\newline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Type of error test used {\it relabs}:") + (radioButtons relabs + ("" " D, default (mixed)" mix) + ("" " A, absolute" abs) + ("" " R, relative" rel)) + (text . "\blankline ") + (text . "\newline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Ifail value:") + (radioButtons ifail + ("" " -1, Print error messages" minusOne) + ("" " 1, Suppress error messages" one))) + htMakeDoneButton('"Continue", 'd02cjfSolve) + htShowPage() + +d02cjfSolve htPage == + x := htpLabelInputString(htPage,'x) + xend := htpLabelInputString(htPage,'xend) + n := + $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'n) + objValUnwrap htpLabelSpadValue(htPage, 'n) + tol := htpLabelInputString(htPage,'tol) + control := htpButtonValue(htPage,'relabs) + relabs := + control = 'mix => '"D" + control = 'abs => '"A" + '"R" + error := htpButtonValue(htPage,'ifail) + ifail := + error = 'one => '1 + '-1 + n = '3 => d02cjfDefaultSolve(htPage,x,xend,tol,relabs,ifail) + funcList := + "append"/[fa(i) for i in 1..n] where fa(i) == + prefix := ('"\newline {\em Function ") + prefix := STRCONC(prefix,STRINGIMAGE i,'":} \space{1}") + funct := STRCONC ('"Y[",STRINGIMAGE i ,"]") + nam := INTERN STRCONC ('"n",STRINGIMAGE i) + [['text,:prefix],['bcStrings,[42, funct, nam, 'EM]]] + middle := ('"\blankline \menuitemstyle{} \tab{2} Enter the initial ") + middle := STRCONC(middle,'"values of \htbitmap{yi}: \newline ") + yList := + "append"/[fb(i) for i in 1..n] where fb(i) == + ynam := INTERN STRCONC ('"u",STRINGIMAGE i) + [['bcStrings,[6, 0, ynam, 'F]]] + yList := [['text,:middle],:yList] + mid:= ('"\blankline \menuitemstyle{} \tab{2} Intermediate values of {\it x}") + mid := STRCONC(mid,'" at which \htbitmap{yi} is required: \newline ") + vList := [['bcStrings,[30, "2,4", 'out, 'EM]]] + vList := [['text,:mid],:vList] + midd := ('"\blankline \menuitemstyle{} \tab{2} Enter the function below ") + midd := STRCONC(midd,'"{\em g(x,y)}: \newline ") + uList := [['bcStrings,[30, '"Y[1]", 'g, 'EM]]] + uList := [['text,:midd],:uList] + equationPart := [ + '(domainConditions + (isDomain EM $EmptyMode) + (isDomain S (String)) + (isDomain F (Float)) + (isDomain I (Integer))), + :funcList,:yList,:vList,:uList] + page := htInitPage('"D02CJF - ODEs, IVP, Adams method, until function of solution is zero, intermediate output",nil) + htSay '"\menuitemstyle{}\tab{2} " + htSay '"Enter the functions (i.e. the derivatives) below \htbitmap{fi} " + htSay '"as functions of Y[1]...Y[n]: " + htSay '"\newline " + htMakePage equationPart + htMakeDoneButton('"Continue",'d02cjfGen) + htpSetProperty(page,'x,x) + htpSetProperty(page,'xend,xend) + htpSetProperty(page,'n,n) + htpSetProperty(page,'tol,tol) + htpSetProperty(page,'relabs,relabs) + htpSetProperty(page,'ifail,ifail) + htpSetProperty(page,'inputArea, htpInputAreaAlist htPage) + htShowPage() + +d02cjfDefaultSolve(htPage,x,xend,tol,relabs,ifail) == + n := '3 + page := htInitPage('"D02CJF - ODEs, IVP, Adams method, until function of solution is zero, intermediate output",nil) + htMakePage '( + (domainConditions + (isDomain EM $EmptyMode) + (isDomain F (Float)) + (isDomain I (Integer))) + (text . "\newline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Enter the functions (i.e. the derivatives) below \htbitmap{fi} ") + (text . "as functions of Y[1]...Y[n]: ") + (text . "\newline {\em Function 1:} \space{1}") + (bcStrings (44 "tan(Y[3])" f1 EM)) + (text . "\newline {\em Function 2:} \space{1}") + (bcStrings (44 "-0.032*tan(Y[3])/Y[2] -0.02*Y[2]/cos(Y[3])" f2 EM)) + (text . "\newline {\em Function 3:} \space{1}") + (bcStrings (44 "-0.032/(Y[2]**2)" f3 EM)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Enter the initial values of \htbitmap{yi}:") + (text . "\newline ") + (bcStrings (8 "0.5" y1 EM)) + (bcStrings (8 "0.5" y2 EM)) + (bcStrings (8 "\%pi*0.2" y3 EM)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2} Intermediate") + (text . " values of {\it x} at which \htbitmap{yi} is required:") + (text . "\newline ") + (bcStrings (30 "2,4,6,8" out EM)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Enter the function below {\em g(x,y)}: ") + (text . "\newline ") + (bcStrings (30 "Y[1]" g EM))) + htpSetProperty(page,'x,x) + htpSetProperty(page,'xend,xend) + htpSetProperty(page,'n,n) + htpSetProperty(page,'tol,tol) + htpSetProperty(page,'relabs,relabs) + htpSetProperty(page,'ifail,ifail) + htMakeDoneButton('"Continue",'d02cjfGen) + htpSetProperty(page,'inputArea, htpInputAreaAlist htPage) + htShowPage() + +d02cjfGen htPage == + x := htpProperty(htPage, 'x) + xend := htpProperty(htPage, 'xend) + n := htpProperty(htPage, 'n) + tol := htpProperty(htPage, 'tol) + relabs := htpProperty(htPage, 'relabs) + ifail := htpProperty(htPage, 'ifail) + alist := htpInputAreaAlist htPage + y := alist + g := ((first y).1) + y := rest y + outp := ((first y).1) + oList := [outp,:oList] + ostring := bcwords2liststring oList + -- This is distictly horrible! OUTP is a comma-seperated string so we + -- count up the commas to see how many elements it has. We return this + -- quantity plus 1 since the ASP OUTPUT is always called at least once. + numberOfPoints := + ZEROP LENGTH(outp) => 1 + 2+COUNT(CHARACTER(44),outp) + y := rest y + for i in 1..n repeat + ytemp := STRCONC((first y).1," ") + yList := [ytemp,:yList] + y := rest y + ystring := bcwords2liststring yList + while y repeat + f := STRCONC((first y).1," ") + fList := [f,:fList] + y := rest y + fstring := bcwords2liststring fList + prefix := STRCONC("d02cjf(",xend,", ",STRINGIMAGE numberOfPoints ,", ", STRINGIMAGE n,", ",tol,",_"",relabs) + mid := STRCONC("_", ",x ,", [", ystring,"],",STRINGIMAGE ifail) + mid := STRCONC(mid,",(",g,"::Expression Float)::ASP9('G),(",fstring) + end := STRCONC("::Vector Expression Float)::ASP7('FCN),(",ostring) + end := STRCONC(end,"::Vector MachineFloat)::ASP8('OUTPUT))") + linkGen STRCONC(prefix,mid,end) + + + +d02ejf() == + htInitPage('"D02EJF - ODEs, stiff IVP, BDF method, until function of solution is zero, intermediate output",nil) + htMakePage '( + (domainConditions + (isDomain PI (PositiveInteger))) + (text . "\windowlink{Manual Page}{manpageXXd02ejf} for this routine ") + (text . "\newline ") + (text . "\lispwindowlink{Browser operation page}{(|oPageFrom| '|d02ejf| '|NagOrdinaryDifferentialEquationsPackage|)} for this routine") + (text . "\newline \horizontalline ") + (text . "\newline ") + (text . "D02EJF integrates a system of {\em n} ordinary differential ") + (text . "equations, {\htbitmap{yi}}' = {\htbitmap{fi}}(x,y), for {\it i} ") + (text . "= 1,,2,...,{\it n}, over a range with given initial conditions") + (text . " using backward differentiation formulae until a specified ") + (text . "function {\em g(x,y)} of the solution is zero; the solution may ") + (text . "be output at specified points. \blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Initial value of {\it x}:") + (text . "\newline\tab{2} ") + (bcStrings (5 "0.0" x F)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "End of integration range {\it xend}:") + (text . "\newline\tab{2} ") + (bcStrings (5 "10.0" xend F)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Number of differential equations {\it n}:") + (text . "\newline\tab{2} ") + (bcStrings (5 3 n PI)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "\newline Tolerance required {\it tol}: ") + (text . "\newline\tab{2} ") + (bcStrings (10 "0.0001" tol F)) + (text . "\blankline ") + (text . "\newline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Type of error test used {\it relabs}:") + (radioButtons relabs + ("" " D, default (mixed)" mix) + ("" " A, absolute" abs) + ("" " R, relative" rel)) + (text . "\blankline ") + (text . "\newline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Ifail value:") + (radioButtons ifail + ("" " -1, Print error messages" minusOne) + ("" " 1, Suppress error messages" one))) + htMakeDoneButton('"Continue", 'd02ejfSolve) + htShowPage() + +d02ejfSolve htPage == + x := htpLabelInputString(htPage,'x) + xend := htpLabelInputString(htPage,'xend) + n := + $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'n) + objValUnwrap htpLabelSpadValue(htPage, 'n) + tol := htpLabelInputString(htPage,'tol) + control := htpButtonValue(htPage,'relabs) + relabs := + control = 'mix => '"D" + control = 'abs => '"A" + '"R" + iw := (n + 12) * n + 50 + error := htpButtonValue(htPage,'ifail) + ifail := + error = 'one => '1 + '-1 + n = '3 => d02ejfDefaultSolve(htPage,x,xend,tol,relabs,iw,ifail) + funcList := + "append"/[fa(i) for i in 1..n] where fa(i) == + prefix := ('"\newline {\em Function ") + prefix := STRCONC(prefix,STRINGIMAGE i,'":} \space{1}") + funct := STRCONC ('"Y[",STRINGIMAGE i ,"]") + nam := INTERN STRCONC ('"n",STRINGIMAGE i) + [['text,:prefix],['bcStrings,[42, funct, nam, 'EM]]] + middle := ('"\blankline \menuitemstyle{} \tab{2} Enter the initial ") + middle := STRCONC(middle,'"values of \htbitmap{yi}: \newline ") + yList := + "append"/[fb(i) for i in 1..n] where fb(i) == + ynam := INTERN STRCONC ('"u",STRINGIMAGE i) + [['bcStrings,[6, 0, ynam, 'F]]] + yList := [['text,:middle],:yList] + mid:= ('"\blankline \menuitemstyle{} \tab{2} Intermediate values of {\it x}") + mid := STRCONC(mid,'" at which \htbitmap{yi} is required: \newline ") + vList := [['bcStrings,[30, "2,4,6,8", 'out, 'EM]]] + vList := [['text,:mid],:vList] + midd := ('"\blankline \menuitemstyle{} \tab{2} Enter the function below ") + midd := STRCONC(midd,'"{\em g(x,y)}: \newline ") + uList := [['bcStrings,[30, '"Y[1]", 'g, 'EM]]] + uList := [['text,:midd],:uList] + equationPart := [ + '(domainConditions + (isDomain EM $EmptyMode) + (isDomain S (String)) + (isDomain F (Float)) + (isDomain I (Integer))), + :funcList,:yList,:vList,:uList] + page := htInitPage('"D02EJF - ODEs, stiff IVP, BDF method, until function of solution is zero, intermediate output",nil) + htSay '"\menuitemstyle{}\tab{2} " + htSay '"Enter the functions (i.e. the derivatives) below \htbitmap{fi} " + htSay '"as functions of Y[1]...Y[n]: " + htSay '"\newline " + htMakePage equationPart + htSay '"\blankline {\em Note:} PEDERV is automatically generated using the vector " + htSay '"of derivatives given above. " + htMakeDoneButton('"Continue",'d02ejfGen) + htpSetProperty(page,'x,x) + htpSetProperty(page,'xend,xend) + htpSetProperty(page,'n,n) + htpSetProperty(page,'tol,tol) + htpSetProperty(page,'relabs,relabs) + htpSetProperty(page,'iw,iw) + htpSetProperty(page,'ifail,ifail) + htpSetProperty(page,'inputArea, htpInputAreaAlist htPage) + htShowPage() + +d02ejfDefaultSolve(htPage,x,xend,tol,relabs,iw,ifail) == + n := '3 + page := htInitPage('"D02EJF - ODEs, stiff IVP, BDF method, until function of solution is zero, intermediate output",nil) + htMakePage '( + (domainConditions + (isDomain EM $EmptyMode) + (isDomain F (Float)) + (isDomain I (Integer))) + (text . "\newline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Enter the functions (i.e. the derivatives) below \htbitmap{fi} ") + (text . "as functions of Y[1]...Y[n]: ") + (text . "\newline {\em Function 1:} \space{1}") + (bcStrings (44 "-0.04*Y[1]+1.0E4*Y[2]*Y[3]" f1 EM)) + (text . "\newline {\em Function 2:} \space{1}") + (bcStrings (44 "0.04*Y[1]-1.0E4*Y[2]*Y[3]-3.0E7*Y[2]*Y[2]" f2 EM)) + (text . "\newline {\em Function 3:} \space{1}") + (bcStrings (44 "3.0E7*Y[2]*Y[2]" f3 EM)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Enter the initial values of \htbitmap{yi}:") + (text . "\newline ") + (bcStrings (8 "1.0" y1 EM)) + (bcStrings (8 "0.0" y2 EM)) + (bcStrings (8 "0.0" y3 EM)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2} Intermediate") + (text . " values of {\it x} at which \htbitmap{yi} is required:") + (text . "\newline ") + (bcStrings (30 "2,4,6,8" out EM)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Enter the function below {\em g(x,y)}: ") + (text . "\newline ") + (bcStrings (30 "Y[1]-0.9" g EM)) + (text . "\blankline ") + (text . "{\em Note:} PEDERV is automatically generated using the vector ") + (text . "of derivatives given above. ")) + htpSetProperty(page,'x,x) + htpSetProperty(page,'xend,xend) + htpSetProperty(page,'n,n) + htpSetProperty(page,'tol,tol) + htpSetProperty(page,'relabs,relabs) + htpSetProperty(page,'iw,iw) + htpSetProperty(page,'ifail,ifail) + htMakeDoneButton('"Continue",'d02ejfGen) + htpSetProperty(page,'inputArea, htpInputAreaAlist htPage) + htShowPage() + +d02ejfGen htPage == + x := htpProperty(htPage, 'x) + xend := htpProperty(htPage, 'xend) + n := htpProperty(htPage, 'n) + tol := htpProperty(htPage, 'tol) + relabs := htpProperty(htPage, 'relabs) + iw := htpProperty(htPage, 'iw) + ifail := htpProperty(htPage, 'ifail) + alist := htpInputAreaAlist htPage + y := alist + g := ((first y).1) + y := rest y + outp := ((first y).1) + oList := [outp,:oList] + ostring := bcwords2liststring oList + -- This is distictly horrible! OUTP is a comma-seperated string so we + -- count up the commas to see how many elements it has. We return this + -- quantity plus 1 since the ASP OUTPUT is always called at least once. + numberOfPoints := + ZEROP LENGTH(outp) => 1 + 2+COUNT(CHARACTER(44),outp) + y := rest y + for i in 1..n repeat + ytemp := STRCONC((first y).1," ") + yList := [ytemp,:yList] + y := rest y + ystring := bcwords2liststring yList + while y repeat + f := STRCONC((first y).1," ") + fList := [f,:fList] + y := rest y + fstring := bcwords2liststring fList + prefix := STRCONC("d02ejf(",xend,", ",STRINGIMAGE numberOfPoints,", ", STRINGIMAGE n,",_"",relabs,"_", ") + mid:=STRCONC(STRINGIMAGE iw,", ",x ,", [", ystring,"], ",tol,", ") + mid := STRCONC(mid,STRINGIMAGE ifail,",(",g,"::Expression Float)::ASP9(G),(") + end := STRCONC(fstring,"::Vector Expression Float)::ASP7('FCN),(",fstring) + end := STRCONC(end,"::Vector Expression Float)::ASP31('PEDERV),(",ostring) + end := STRCONC(end,"::Vector MachineFloat)::ASP8('OUTPUT))") + linkGen STRCONC(prefix,mid,end) + +d02gaf() == + htInitPage('"D02GAF - ODEs, boundary value problem, finite difference technique with deferred correction, simple nonlinear problem", nil) + htMakePage '( + (domainConditions + (isDomain PI (PositiveInteger))) + (text . "\windowlink{Manual Page}{manpageXXd02gaf} for this routine ") + (text . "\newline ") + (text . "\lispwindowlink{Browser operation page}{(|oPageFrom| '|d02gaf| '|NagOrdinaryDifferentialEquationsPackage|)} for this routine") + (text . "\newline \horizontalline ") + (text . "\newline ") + (text . "D02GAF solves a two-point boundary value problem for a system ") + (text . "of n ODEs \center{\htbitmap{d02gaf},} for i = 1,2,...,n, on ") + (text . "the range [a,b] with assigned boundary conditions using a ") + (text . "deferred correction technique and a Newton iteration; ") + (text . "the solution is computed on a mesh. ") + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Enter the number of equations in the system {\it n}:") + (text . "\newline\tab{2} ") + (bcStrings (5 3 n PI)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "\newline Left hand boundary point {\it a}: ") + (text . "\tab{32} \menuitemstyle{}\tab{34} ") + (text . "Right hand boundary {\it b}:") + (text . "\newline\tab{2} ") + (bcStrings (10 "0.0" a F)) + (text . "\tab{34} ") + (bcStrings (10 "10.0" b F)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "\newline Max number of mesh points {\it mnp}:") + (text . "\tab{32} \menuitemstyle{}\tab{34} ") + (text . "Number of points {\it np} ({\it np} = 0 or {\it np} ") + (text . "\htbitmap{great=} 4): ") + (text . "\newline\tab{2} ") + (bcStrings (10 64 mnp PI)) + (text . "\tab{34} ") + (bcStrings (10 26 np PI)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Accuracy required {\it tol}:") + (text . "\newline\tab{2} ") + (bcStrings (10 "1.0e-3" tol F)) + (text . "\blankline ") + (text . "\newline \tab{2} ") + (text . "Ifail is input in three components: ") + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "{\it a} ") + (radioButtons afail + ("" " 0, hard failure" azero) + ("" " 1, soft failure" aone)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "{\it b} ") + (radioButtons bfail + ("" " 1, print error messages" bone) + ("" " 0, suppress error messages" bzero)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "{\it c} ") + (radioButtons cfail + ("" " 1, print warning messages" cone) + ("" " 0, suppress warning messages" czero))) + htMakeDoneButton('"Continue", 'd02gafSolve) + htShowPage() + +d02gafSolve htPage == + n := + $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'n) + objValUnwrap htpLabelSpadValue(htPage, 'n) + a := htpLabelInputString(htPage,'a) + b := htpLabelInputString(htPage,'b) + mnp := + $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'mnp) + objValUnwrap htpLabelSpadValue(htPage, 'mnp) + np := + $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'np) + objValUnwrap htpLabelSpadValue(htPage, 'np) + lw := mnp * (3*n*n + 6*n + 2) + 4*n*n + 4*n + liw := mnp * (2*n + 1) + n*n + 4*n + 2 + tol := htpLabelInputString(htPage,'tol) + aerror := htpButtonValue(htPage,'afail) + afail := + aerror = 'azero => '0 + '1 + berror := htpButtonValue(htPage,'bfail) + bfail := + berror = 'bone => '1 + '0 + cerror := htpButtonValue(htPage,'cfail) + cfail := + cerror = 'cone => '1 + '0 + ifail := 100*cfail + 10*bfail + afail + n = '3 => d02gafDefaultSolve(htPage,a,b,mnp,np,lw,liw,tol,ifail) + funcList := + "append"/[fa(i) for i in 1..n] where fa(i) == + prefix := ('"\newline {\em Function ") + prefix := STRCONC(prefix,STRINGIMAGE i,'":} \space{1}") + funct := STRCONC ('"Y[",STRINGIMAGE i ,"]") + nam := INTERN STRCONC ('"n",STRINGIMAGE i) + [['text,:prefix],['bcStrings,[42, funct, nam, 'EM]]] + middle := ('"\blankline \menuitemstyle{} \tab{2} Enter known or estimated ") + middle := STRCONC(middle,'"values of \htbitmap{yi} at a and b, ") + middle := STRCONC(middle,"{\it U(n,2)}. [\htbitmap{yi}(a) in the first ") + middle := STRCONC(middle,"column, \htbitmap{yi}(b) in the second.] ") + middle := STRCONC(middle,"\newline ") + uList := + "append"/[fb(i) for i in 1..n] where fb(i) == + labelList := + "append"/[fc(i,j) for j in 1..2] where fc(i,j) == + unam := INTERN STRCONC ('"u",STRINGIMAGE i,STRINGIMAGE j) + [['bcStrings,[6, 0, unam, 'F]]] + prefix := ('"\newline ") + labelList := [['text,:prefix],:labelList] + uList := [['text,:middle],:uList] + mid := ('"\blankline \menuitemstyle{} \tab{2} Enter {\it V(n,2)}. ") + mid := STRCONC(mid,'"If U(i,j) is known V(i,j) ") + mid := STRCONC(mid,'"= 0.0, else V(i,j) = 1.0. \newline ") + vList := + "append"/[fd(i) for i in 1..n] where fd(i) == + labelList := + "append"/[fe(i,j) for j in 1..2] where fe(i,j) == + vnam := INTERN STRCONC ('"v",STRINGIMAGE i,STRINGIMAGE j) + [['bcStrings,[6, 0, vnam, 'F]]] + prefix := ('"\newline ") + labelList := [['text,:prefix],:labelList] + vList := [['text,:mid],:vList] + xList := + "append"/[ff(i) for i in 1..mnp] where ff(i) == + xnam := INTERN STRCONC ('"x",STRINGIMAGE i) + [['bcStrings,[8, "0.0", xnam, 'F]]] + end := ('"\blankline \menuitemstyle{} \tab{2} Enter the initial mesh ") + end := STRCONC(end,'"{\it X(mnp)}: \newline ") + xList := [['text,:end],:xList] + equationPart := [ + '(domainConditions + (isDomain EM $EmptyMode) + (isDomain S (String)) + (isDomain F (Float)) + (isDomain I (Integer))), + :funcList,:uList,:vList,:xList] + page := htInitPage('"D02GAF - ODEs, boundary value problem, finite difference technique with deferred correction, simple nonlinear problem", nil) + htSay '"\menuitemstyle{}\tab{2} " + htSay '"Enter the functions (i.e. the derivatives) below as functions of " + htSay '"Y[1]...Y[n]: " + htSay '"\newline " + htMakePage equationPart + htMakeDoneButton('"Continue",'d02gafGen) + htpSetProperty(page,'n,n) + htpSetProperty(page,'a,a) + htpSetProperty(page,'b,b) + htpSetProperty(page,'mnp,mnp) + htpSetProperty(page,'np,np) + htpSetProperty(page,'lw,lw) + htpSetProperty(page,'liw,liw) + htpSetProperty(page,'tol,tol) + htpSetProperty(page,'ifail,ifail) + htpSetProperty(page,'inputArea, htpInputAreaAlist htPage) + htShowPage() + +d02gafDefaultSolve(htPage,a,b,mnp,np,lw,liw,tol,ifail) == + n := '3 + page := htInitPage('"D02GAF - ODEs, boundary value problem, finite difference technique with deferred correction, simple nonlinear problem", nil) + htMakePage '( + (domainConditions + (isDomain EM $EmptyMode) + (isDomain F (Float)) + (isDomain I (Integer))) + (text . "\newline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Enter the functions (i.e. the derivatives) below ") + (text . "as functions of Y[1]...Y[n]: ") + (text . "\newline ") + (text . "\newline {\em Function 1:} \space{1}") + (bcStrings (42 "Y[2]" f1 EM)) + (text . "\newline {\em Function 2:} \space{1}") + (bcStrings (42 "Y[3]" f2 EM)) + (text . "\newline {\em Function 3:} \space{1}") + (bcStrings (42 "-Y[1]*Y[3]-0.2*(1-Y[2]*Y[2])" f3 EM)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Enter known or estimated values of \htbitmap{yi} at a and b,") + (text . " {\it U(n,2)}. ") + (text . " [\htbitmap{yi}(a) in the first column, \htbitmap{yi}(b) ") + (text . "in the second.] \newline ") + (bcStrings (6 "0" u11 F)) + (bcStrings (6 "10" u21 F)) + (text . "\newline ") + (bcStrings (6 "0" u12 F)) + (bcStrings (6 "1" u22 F)) + (text . "\newline ") + (bcStrings (6 "0" u13 F)) + (bcStrings (6 "0" u23 F)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Enter {\it V(n,2)}. ") + (text . "If U(i,j) is known V(i,j) = 0.0, else V(i,j) = 1.0: \newline") + (bcStrings (6 "0.0" v11 F)) + (bcStrings (6 "1.0" v21 F)) + (text . "\newline ") + (bcStrings (6 "0.0" v12 F)) + (bcStrings (6 "0.0" v22 F)) + (text . "\newline ") + (bcStrings (6 "1.0" v13 F)) + (bcStrings (6 "1.0" v23 F)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2} ") + (text . "Enter the initial mesh {\it X(mnp)}: ") + (text . "\newline ") + (bcStrings (8 "0.0" x1 F)) + (bcStrings (8 "0.4" x2 F)) + (bcStrings (8 "0.8" x3 F)) + (bcStrings (8 "1.2" x4 F)) + (bcStrings (8 "1.6" x5 F)) + (bcStrings (8 "2.0" x6 F)) + (bcStrings (8 "2.4" x7 F)) + (bcStrings (8 "2.8" x8 F)) + (bcStrings (8 "3.2" x9 F)) + (bcStrings (8 "3.6" x10 F)) + (bcStrings (8 "4.0" x11 F)) + (bcStrings (8 "4.4" x12 F)) + (bcStrings (8 "4.8" x13 F)) + (bcStrings (8 "5.2" x14 F)) + (bcStrings (8 "5.6" x15 F)) + (bcStrings (8 "6.0" x16 F)) + (bcStrings (8 "6.4" x17 F)) + (bcStrings (8 "6.8" x18 F)) + (bcStrings (8 "7.2" x19 F)) + (bcStrings (8 "7.6" x20 F)) + (bcStrings (8 "8.0" x21 F)) + (bcStrings (8 "8.4" x22 F)) + (bcStrings (8 "8.8" x23 F)) + (bcStrings (8 "9.2" x24 F)) + (bcStrings (8 "9.6" x25 F)) + (bcStrings (8 "10.0" x26 F)) + (bcStrings (8 "0.0" x27 F)) + (bcStrings (8 "0.0" x28 F)) + (bcStrings (8 "0.0" x29 F)) + (bcStrings (8 "0.0" x30 F)) + (bcStrings (8 "0.0" x31 F)) + (bcStrings (8 "0.0" x32 F)) + (bcStrings (8 "0.0" x33 F)) + (bcStrings (8 "0.0" x34 F)) + (bcStrings (8 "0.0" x35 F)) + (bcStrings (8 "0.0" x36 F)) + (bcStrings (8 "0.0" x37 F)) + (bcStrings (8 "0.0" x38 F)) + (bcStrings (8 "0.0" x39 F)) + (bcStrings (8 "0.0" x40 F)) + (bcStrings (8 "0.0" x41 F)) + (bcStrings (8 "0.0" x42 F)) + (bcStrings (8 "0.0" x43 F)) + (bcStrings (8 "0.0" x44 F)) + (bcStrings (8 "0.0" x45 F)) + (bcStrings (8 "0.0" x46 F)) + (bcStrings (8 "0.0" x47 F)) + (bcStrings (8 "0.0" x48 F)) + (bcStrings (8 "0.0" x49 F)) + (bcStrings (8 "0.0" x50 F)) + (bcStrings (8 "0.0" x51 F)) + (bcStrings (8 "0.0" x52 F)) + (bcStrings (8 "0.0" x53 F)) + (bcStrings (8 "0.0" x54 F)) + (bcStrings (8 "0.0" x55 F)) + (bcStrings (8 "0.0" x56 F)) + (bcStrings (8 "0.0" x57 F)) + (bcStrings (8 "0.0" x58 F)) + (bcStrings (8 "0.0" x59 F)) + (bcStrings (8 "0.0" x60 F)) + (bcStrings (8 "0.0" x61 F)) + (bcStrings (8 "0.0" x62 F)) + (bcStrings (8 "0.0" x63 F)) + (bcStrings (8 "0.0" x64 F))) + htpSetProperty(page,'n,n) + htpSetProperty(page,'a,a) + htpSetProperty(page,'b,b) + htpSetProperty(page,'mnp,mnp) + htpSetProperty(page,'np,np) + htpSetProperty(page,'lw,lw) + htpSetProperty(page,'liw,liw) + htpSetProperty(page,'tol,tol) + htpSetProperty(page,'ifail,ifail) + htMakeDoneButton('"Continue",'d02gafGen) + htpSetProperty(page,'inputArea, htpInputAreaAlist htPage) + htShowPage() + +d02gafGen htPage == + n := htpProperty(htPage, 'n) + a := htpProperty(htPage, 'a) + b := htpProperty(htPage, 'b) + mnp := htpProperty(htPage, 'mnp) + np := htpProperty(htPage, 'np) + lw := htpProperty(htPage, 'lw) + liw := htpProperty(htPage, 'liw) + ifail := htpProperty(htPage,'ifail) + tol := htpProperty(htPage,'tol) + alist := htpInputAreaAlist htPage + y := alist + for i in 1..mnp repeat + x := STRCONC((first y).1," ") + xList := [x,:xList] + y := rest y + xstring := bcwords2liststring xList + for i in 1..n repeat + for j in 1..2 repeat + v := STRCONC((first y).1," ") + rowList := [v,:rowList] + y := rest y + vList := [:vList,rowList] + rowList := [] + for i in 1..n repeat + for j in 1..2 repeat + u := STRCONC((first y).1," ") + rowList := [u,:rowList] + y := rest y + uList := [:uList,rowList] + rowList := [] + vList := reverse vList + uList := reverse uList + vstring := bcwords2liststring [bcwords2liststring x for x in vList] + ustring := bcwords2liststring [bcwords2liststring x for x in uList] + while y repeat + f := STRCONC((first y).1," ") + fList := [f,:fList] + y := rest y + fstring := bcwords2liststring fList + Y:='Y + prefix := STRCONC("d02gaf(",ustring,", ",vstring,", ",STRINGIMAGE n,", ") + prefix := STRCONC(prefix,a,", ",b,", ",tol,", ") + prefix := STRCONC(prefix,STRINGIMAGE mnp,", ",STRINGIMAGE lw,", ") + prefix := STRCONC(prefix,STRINGIMAGE liw,", [",xstring,"], ",STRINGIMAGE np) + end:=STRCONC (",",STRINGIMAGE ifail,",(",fstring,"::Vector Expression Float") + linkGen STRCONC (prefix,end,")::ASP7('FCN))") + +d02gbf() == + htInitPage('"D02GBF - ODEs, boundary value problem, finite difference technique with deferred correction, general nonlinear problem", nil) + htMakePage '( + (domainConditions + (isDomain PI (PositiveInteger))) + (text . "\windowlink{Manual Page}{manpageXXd02gbf} for this routine ") + (text . "\newline ") + (text . "\lispwindowlink{Browser operation page}{(|oPageFrom| '|d02gbf| '|NagOrdinaryDifferentialEquationsPackage|)} for this routine") + (text . "\newline \horizontalline ") + (text . "\newline ") + (text . "D02GBF solves a general linear two-point boundary value problem ") + (text . "for a system of n ODEs {\it y' = F(x)y + g(x)} on the range ") + (text . "[a,b] with boundary conditions {\it Cy(a) + Dy(b) = \gamma} ") + (text . "using a deferred correction technique.") + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Enter the number of equations in the system {\it n}:") + (text . "\newline\tab{2} ") + (bcStrings (5 2 n PI)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "\newline Left hand boundary point {\it a}: ") + (text . "\tab{32} \menuitemstyle{}\tab{34} ") + (text . "Right hand boundary {\it b}:") + (text . "\newline\tab{2} ") + (bcStrings (10 "0.0" a F)) + (text . "\tab{34} ") + (bcStrings (10 "1.0" b F)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "\newline Max number of mesh points {\it mnp}:") + (text . "\tab{32} \menuitemstyle{}\tab{34} ") + (text . "Number of points {\it np}: ") + (text . "\newline\tab{2} ") + (bcStrings (10 70 mnp PI)) + (text . "\tab{34} ") + (bcStrings (10 0 np PI)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Accuracy required {\it tol}:") + (text . "\newline\tab{2} ") + (bcStrings (10 "1.0e-3" tol F)) + (text . "\blankline ") + (text . "\newline \tab{2} ") + (text . "Ifail is input in three components: ") + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "{\it a} ") + (radioButtons afail + ("" " 0, hard failure" azero) + ("" " 1, soft failure" aone)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "{\it b} ") + (radioButtons bfail + ("" " 1, print error messages" bone) + ("" " 0, suppress error messages" bzero)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "{\it c} ") + (radioButtons cfail + ("" " 1, print warning messages" cone) + ("" " 0, suppress warning messages" czero))) + htMakeDoneButton('"Continue", 'd02gbfSolve) + htShowPage() + +d02gbfSolve htPage == + n := + $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'n) + objValUnwrap htpLabelSpadValue(htPage, 'n) + a := htpLabelInputString(htPage,'a) + b := htpLabelInputString(htPage,'b) + mnp := + $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'mnp) + objValUnwrap htpLabelSpadValue(htPage, 'mnp) + np := + $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'np) + objValUnwrap htpLabelSpadValue(htPage, 'np) + lw := mnp * (3*n*n + 5*n + 2) + 3*n*n + 5*n + liw := mnp * (2*n + 1) + n + tol := htpLabelInputString(htPage,'tol) + aerror := htpButtonValue(htPage,'afail) + afail := + aerror = 'azero => '0 + '1 + berror := htpButtonValue(htPage,'bfail) + bfail := + berror = 'bone => '1 + '0 + cerror := htpButtonValue(htPage,'cfail) + cfail := + cerror = 'cone => '1 + '0 + ifail := 100*cfail + 10*bfail + afail + n = '2 => d02gbfDefaultSolve(htPage,a,b,mnp,np,lw,liw,tol,ifail) + cList := + "append"/[fa(i,n) for i in 1..n] where fa(i,n) == + labelList := + "append"/[fb(i,j) for j in 1..n] where fb(i,j) == + cnam := INTERN STRCONC ('"c",STRINGIMAGE i,STRINGIMAGE j) + [['bcStrings,[6, 0, cnam, 'F]]] + prefix := ('"\newline ") + labelList := [['text,:prefix],:labelList] + middle := ('"\blankline \menuitemstyle{} \tab{2} Enter the matrix {\it D}: ") + middle := STRCONC(middle,"\newline ") + dList := + "append"/[fc(i,n) for i in 1..n] where fc(i,n) == + labelList := + "append"/[fd(i,j) for j in 1..n] where fd(i,j) == + dnam := INTERN STRCONC ('"d",STRINGIMAGE i,STRINGIMAGE j) + [['bcStrings,[6, 0, dnam, 'F]]] + prefix := ('"\newline ") + labelList := [['text,:prefix],:labelList] + dList := [['text,:middle],:dList] + middle := ('"\blankline \menuitemstyle{} \tab{2} Enter the vector \gamma: ") + middle := STRCONC(middle,"\newline ") + gamList := + "append"/[fe(i) for i in 1..n] where fe(i) == + gamnam := INTERN STRCONC ('"gam",STRINGIMAGE i) + [['bcStrings,[6, 0, gamnam, 'F]]] + prefix := ('"\newline ") + gamList := [['text,:middle],:gamList] + middle := ('"\blankline \menuitemstyle{} \tab{2} Enter the matrix ") + middle := STRCONC(middle,"{\it F(x)} from the equation {\it y' =} ") + middle := STRCONC(middle,"{\it F(x)y + g(x)}: \newline ") + fList := + "append"/[ff(i,n) for i in 1..n] where ff(i,n) == + labelList := + "append"/[fg(i,j) for j in 1..n] where fg(i,j) == + fnam := INTERN STRCONC ('"f",STRINGIMAGE i,STRINGIMAGE j) + [['bcStrings,[6, 0, fnam, 'F]]] + prefix := ('"\newline ") + labelList := [['text,:prefix],:labelList] + fList := [['text,:middle],:fList] + mid := ('"\blankline \menuitemstyle{} \tab{2} Enter the vector {\it g(x)}: ") + mid := STRCONC(mid,'"\newline ") + gList := + "append"/[fh(i) for i in 1..n] where fh(i) == + gnam := INTERN STRCONC ('"g",STRINGIMAGE i) + [['bcStrings,[6, 0, gnam, 'F]]] + prefix := ('"\newline ") + gList := [['text,:middle],:gList] + xList := + "append"/[fi(i) for i in 1..mnp] where fi(i) == + xnam := INTERN STRCONC ('"x",STRINGIMAGE i) + [['bcStrings,[8, "0.0", xnam, 'F]]] + end := ('"\blankline \menuitemstyle{} \tab{2} The initial mesh {\it X(mnp)}") + end := STRCONC(end,'", (all entries = 0 if np < 4): \newline ") + xList := [['text,:end],:xList] + equationPart := [ + '(domainConditions + (isDomain EM $EmptyMode) + (isDomain S (String)) + (isDomain F (Float)) + (isDomain I (Integer))), + :cList,:dList,:gamList,:fList,:gList,:xList] + page := htInitPage('"D02GBF - ODEs, boundary value problem, finite difference technique with deferred correction, general nonlinear problem", nil) + htSay '"\menuitemstyle{}\tab{2} " + htSay '"Enter the matrix {\it C} form the equation {\it Cy(a) + Dy(b)} " + htSay '"= \gamma \newline " + htMakePage equationPart + htMakeDoneButton('"Continue",'d02gbfGen) + htpSetProperty(page,'n,n) + htpSetProperty(page,'a,a) + htpSetProperty(page,'b,b) + htpSetProperty(page,'mnp,mnp) + htpSetProperty(page,'np,np) + htpSetProperty(page,'lw,lw) + htpSetProperty(page,'liw,liw) + htpSetProperty(page,'tol,tol) + htpSetProperty(page,'ifail,ifail) + htpSetProperty(page,'inputArea, htpInputAreaAlist htPage) + htShowPage() + +d02gbfDefaultSolve(htPage,a,b,mnp,np,lw,liw,tol,ifail) == + n := '2 + page := htInitPage('"D02GBF - ODEs, boundary value problem, finite difference technique with deferred correction, general nonlinear problem", nil) + htMakePage '( + (domainConditions + (isDomain EM $EmptyMode) + (isDomain F (Float)) + (isDomain I (Integer))) + (text . "\newline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Enter the matrix {\it C} from the equation {\it Cy(a) + Dy(b)} = \gamma:") + (text . "\newline ") + (bcStrings (6 "1" c11 F)) + (bcStrings (6 "0" c12 F)) + (text . "\newline ") + (bcStrings (6 "0" c21 F)) + (bcStrings (6 "0" c22 F)) + (text . "\blankline \menuitemstyle{}\tab{2}") + (text . "Enter the matrix {\it D}: \newline ") + (bcStrings (6 "0" d11 F)) + (bcStrings (6 "0" d12 F)) + (text . "\newline ") + (bcStrings (6 "1" d21 F)) + (bcStrings (6 "0" d22 F)) + (text . "\blankline \menuitemstyle{}\tab{2}") + (text . "Enter the vector \gamma: \newline ") + (bcStrings (6 "0" gam1 F)) + (bcStrings (6 "1" gam2 F)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Enter the matrix {\it F(x)} from the equation {\it y' = F(x)y + g(x)} : ") + (text . "\newline ") + (bcStrings (6 "0" f11 F)) + (bcStrings (6 "1" f12 F)) + (text . "\newline ") + (bcStrings (6 "0" f21 F)) + (bcStrings (6 "-10" f22 F)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Enter the vector {\it g(x)}: ") + (text . "\newline ") + (bcStrings (6 "0" g1 F)) + (bcStrings (6 "0" g2 F)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2} The initial mesh {\it X(mnp)}, ") + (text . "(all entries = 0 if np < 4): \newline ") + (bcStrings (8 "0.0" x1 F)) + (bcStrings (8 "0.0" x2 F)) + (bcStrings (8 "0.0" x3 F)) + (bcStrings (8 "0.0" x4 F)) + (bcStrings (8 "0.0" x5 F)) + (bcStrings (8 "0.0" x6 F)) + (bcStrings (8 "0.0" x7 F)) + (bcStrings (8 "0.0" x8 F)) + (bcStrings (8 "0.0" x9 F)) + (bcStrings (8 "0.0" x10 F)) + (bcStrings (8 "0.0" x11 F)) + (bcStrings (8 "0.0" x12 F)) + (bcStrings (8 "0.0" x13 F)) + (bcStrings (8 "0.0" x14 F)) + (bcStrings (8 "0.0" x15 F)) + (bcStrings (8 "0.0" x16 F)) + (bcStrings (8 "0.0" x17 F)) + (bcStrings (8 "0.0" x18 F)) + (bcStrings (8 "0.0" x19 F)) + (bcStrings (8 "0.0" x20 F)) + (bcStrings (8 "0.0" x21 F)) + (bcStrings (8 "0.0" x22 F)) + (bcStrings (8 "0.0" x23 F)) + (bcStrings (8 "0.0" x24 F)) + (bcStrings (8 "0.0" x25 F)) + (bcStrings (8 "0.0" x26 F)) + (bcStrings (8 "0.0" x27 F)) + (bcStrings (8 "0.0" x28 F)) + (bcStrings (8 "0.0" x29 F)) + (bcStrings (8 "0.0" x30 F)) + (bcStrings (8 "0.0" x31 F)) + (bcStrings (8 "0.0" x32 F)) + (bcStrings (8 "0.0" x33 F)) + (bcStrings (8 "0.0" x34 F)) + (bcStrings (8 "0.0" x35 F)) + (bcStrings (8 "0.0" x36 F)) + (bcStrings (8 "0.0" x37 F)) + (bcStrings (8 "0.0" x38 F)) + (bcStrings (8 "0.0" x39 F)) + (bcStrings (8 "0.0" x40 F)) + (bcStrings (8 "0.0" x41 F)) + (bcStrings (8 "0.0" x42 F)) + (bcStrings (8 "0.0" x43 F)) + (bcStrings (8 "0.0" x44 F)) + (bcStrings (8 "0.0" x45 F)) + (bcStrings (8 "0.0" x46 F)) + (bcStrings (8 "0.0" x47 F)) + (bcStrings (8 "0.0" x48 F)) + (bcStrings (8 "0.0" x49 F)) + (bcStrings (8 "0.0" x50 F)) + (bcStrings (8 "0.0" x51 F)) + (bcStrings (8 "0.0" x52 F)) + (bcStrings (8 "0.0" x53 F)) + (bcStrings (8 "0.0" x54 F)) + (bcStrings (8 "0.0" x55 F)) + (bcStrings (8 "0.0" x56 F)) + (bcStrings (8 "0.0" x57 F)) + (bcStrings (8 "0.0" x58 F)) + (bcStrings (8 "0.0" x59 F)) + (bcStrings (8 "0.0" x60 F)) + (bcStrings (8 "0.0" x61 F)) + (bcStrings (8 "0.0" x62 F)) + (bcStrings (8 "0.0" x63 F)) + (bcStrings (8 "0.0" x64 F)) + (bcStrings (8 "0.0" x65 F)) + (bcStrings (8 "0.0" x66 F)) + (bcStrings (8 "0.0" x67 F)) + (bcStrings (8 "0.0" x68 F)) + (bcStrings (8 "0.0" x69 F)) + (bcStrings (8 "0.0" x70 F))) + htpSetProperty(page,'n,n) + htpSetProperty(page,'a,a) + htpSetProperty(page,'b,b) + htpSetProperty(page,'mnp,mnp) + htpSetProperty(page,'np,np) + htpSetProperty(page,'lw,lw) + htpSetProperty(page,'liw,liw) + htpSetProperty(page,'tol,tol) + htpSetProperty(page,'ifail,ifail) + htMakeDoneButton('"Continue",'d02gbfGen) + htpSetProperty(page,'inputArea, htpInputAreaAlist htPage) + htShowPage() + +d02gbfGen htPage == + n := htpProperty(htPage, 'n) + a := htpProperty(htPage, 'a) + b := htpProperty(htPage, 'b) + mnp := htpProperty(htPage, 'mnp) + np := htpProperty(htPage, 'np) + lw := htpProperty(htPage, 'lw) + liw := htpProperty(htPage, 'liw) + ifail := htpProperty(htPage,'ifail) + tol := htpProperty(htPage,'tol) + alist := htpInputAreaAlist htPage + y := alist + for i in 1..mnp repeat -- matrix + x := STRCONC((first y).1," ") + xList := [x,:xList] + y := rest y + xstring := bcwords2liststring xList + for i in 1..n repeat -- vector g + g := STRCONC((first y).1," ") + gList := [g,:gList] + y := rest y + gstring := bcwords2liststring gList + for i in 1..n repeat -- matrix F + for j in 1..n repeat + f := STRCONC((first y).1," ") + flist := [f,:flist] + y := rest y + fmatlist := [:fmatlist,flist] + flist := [] + fmatlist := reverse fmatlist + fmatstr := bcwords2liststring [bcwords2liststring x for x in fmatlist] + for i in 1..n repeat -- vector gamma + gam := STRCONC((first y).1," ") + gamList := [gam,:gamList] + y := rest y + gamstr := bcwords2liststring gamList + for i in 1..n repeat -- matrix D + for j in 1..n repeat + d := STRCONC((first y).1," ") + dlist := [d,:dlist] + y := rest y + dmatlist := [:dmatlist,dlist] + dlist := [] + dmatlist := reverse dmatlist + dmatstr := bcwords2liststring [bcwords2liststring x for x in dmatlist] + for i in 1..n repeat -- matrix C + for j in 1..n repeat + c := STRCONC((first y).1," ") + clist := [c,:clist] + y := rest y + cmatlist := [:cmatlist,clist] + clist := [] + cmatlist := reverse cmatlist + cmatstr := bcwords2liststring [bcwords2liststring x for x in cmatlist] + prefix := STRCONC("d02gbf(",STRINGIMAGE a,", ",STRINGIMAGE b,", ") + prefix := STRCONC(prefix,STRINGIMAGE n,", ",tol,", ",STRINGIMAGE mnp,", ") + prefix := STRCONC(prefix,STRINGIMAGE lw,", ",STRINGIMAGE liw,", ") + prefix := STRCONC(prefix,cmatstr,"::Matrix DoubleFloat,",dmatstr,"::Matrix DoubleFloat,[",gamstr,"]::Matrix DoubleFloat,[",xstring,"]::Matrix DoubleFloat, ") + mid := STRCONC(STRINGIMAGE np,", ",STRINGIMAGE ifail,", ") + end := STRCONC("(",fmatstr,"::Matrix(Expression(Float)))::ASP77(FCNF),(",gstring) + linkGen STRCONC(prefix,mid,end,"::Vector(Expression(Float)))::ASP78(FCNG))") + +d02kef() == + htInitPage('"D02KEF - 2nd order Sturm-Liouville problem, regular/singular system, finite/infinite range, eigenvalue and eigenfunction, user-specified break-points", nil) + htMakePage '( + (domainConditions + (isDomain PI (PositiveInteger))) + (text . "\windowlink{Manual Page}{manpageXXd02kef} for this routine ") + (text . "\newline ") + (text . "\lispwindowlink{Browser operation page}{(|oPageFrom| '|d02kef| '|NagOrdinaryDifferentialEquationsPackage|)} for this routine") + (text . "\newline \horizontalline ") + (text . "\newline ") + (text . "D02KEF finds a specified eigenvalue \htbitmap{lamdab} of a ") + (text . "regular or second-order Sturm-Liouville system ") + (text . "{\it(p(x)y')' + q(x; \lambda)y = 0} on a finite or infinite ") + (text . "range [a,b]; a Pruefer transformation and shooting method ") + (text . "are used; discontinuities in coefficient functions or their ") + (text . "derivatives are permitted. ") + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Number of points in XPOINT {\it m}:") + (text . "\newline\tab{2} ") + (bcStrings (6 5 m PI)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "\newline Index of the `break-point' {\it match}:") + (text . "\newline\tab{2} ") + (bcStrings (6 0 match PI)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "\newline Index of the required eigenvalue {\it k}:") + (text . "\newline\tab{2} ") + (bcStrings (6 11 k PI)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Accuracy required {\it tol}:") + (text . "\newline\tab{2} ") + (bcStrings (10 "0.0001" tol F)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} \newline ") + (text . "Eigenvalue estimate {\it elam}: ") + (text . "\tab{32} \menuitemstyle{}\tab{34} ") + (text . "Scale of the problem {\it delam}: ") + (text . "\newline\tab{2} ") + (bcStrings (10 "14" elam F)) + (text . "\tab{34} ") + (bcStrings (10 "1" delam F)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} \newline ") + (text . "Max iterations {\it maxit}:") + (text . "\tab{32} \menuitemstyle{}\tab{34} ") + (text . "Max COEFFN calls {\it maxfun}:") + (text . "\newline\tab{2} ") + (bcStrings (10 0 maxit PI)) + (text . "\tab{34} ") + (bcStrings (10 0 maxfun PI)) + (text . "\blankline ") + (text . "\tab{2} \newline {\it Note:} no bound is assumed ") + (text . "if maxit = 0 \blankline ") + (text . "\newline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Ifail value:") + (radioButtons ifail + ("" " -1, Print error messages" minusOne) + ("" " 1, Suppress error messages" one))) + htMakeDoneButton('"Continue", 'd02kefSolve) + htShowPage() + +d02kefSolve htPage == + m := + $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'm) + objValUnwrap htpLabelSpadValue(htPage, 'm) + match := + $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'match) + objValUnwrap htpLabelSpadValue(htPage, 'match) + k := + $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'k) + objValUnwrap htpLabelSpadValue(htPage, 'k) + tol := htpLabelInputString(htPage,'tol) + elam := htpLabelInputString(htPage,'elam) + delam := htpLabelInputString(htPage,'delam) + maxit := + $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'maxit) + objValUnwrap htpLabelSpadValue(htPage, 'maxit) + maxfun := + $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'maxfun) + objValUnwrap htpLabelSpadValue(htPage, 'maxfun) + error := htpButtonValue(htPage,'ifail) + ifail := + error = 'minusOne => '-1 + '1 + m = '5 =>d02kefDefaultSolve(htPage,match,k,tol,elam,delam,maxit,maxfun,ifail) + xpList := + "append"/[fa(i) for i in 1..m] where fa(i) == + xpnam := INTERN STRCONC ('"xp",STRINGIMAGE i) + [['bcStrings,[10, "0.0", xpnam, 'EM]]] + middle:=('"\blankline \menuitemstyle{} \tab{2} Value of {\it p} for COEFFN:") + middle := STRCONC(middle,"\newline ") + cList := [['text,:middle],['bcStrings,[42, "0.0", 'c1, 'EM]]] + middle:=('"\blankline \menuitemstyle{} \tab{2} Value of {\it q} for COEFFN:") + middle := STRCONC(middle,"\newline ") + c1List := [['text,:middle],['bcStrings,[42, "0.0", 'c2, 'EM]]] + cList := [:cList,:c1List] + middle:=('"\blankline \menuitemstyle{} \tab{2} Value of {\it dqdl}") + middle := STRCONC(middle," for COEFFN: \newline ") + c2List := [['text,:middle],['bcStrings,[42, "0.0", 'c3, 'EM]]] + cList := [:cList,:c2List] + middle:=('"\blankline \menuitemstyle{} \tab{2} Values of YL(1) & YL(2) ") + middle := STRCONC(middle,"for BDYVAL: \newline ") + ylList := + "append"/[fb(i) for i in 1..2] where fb(i) == + ylnam := INTERN STRCONC ('"yl",STRINGIMAGE i) + [['bcStrings,[42, "0.0", ylnam, 'EM]]] + ylList := [['text,:middle],:ylList] + middle:=('"\blankline \menuitemstyle{} \tab{2} Values of YR(1) & YR(2) ") + middle := STRCONC(middle,"for BDYVAL: \newline ") + yrList := + "append"/[fc(i) for i in 1..2] where fc(i) == + yrnam := INTERN STRCONC ('"yr",STRINGIMAGE i) + [['bcStrings,[42, "0.0", yrnam, 'EM]]] + yrList := [['text,:middle],:yrList] + middle:=('"\blankline \menuitemstyle{} \tab{2} Maximum step size ") + middle := STRCONC(middle,"{\it hmax(2,m)}: \newline ") + hList := + "append"/[fd(i,m) for i in 1..2] where fd(i,m) == + labelList := + "append"/[fe(i,j) for j in 1..m] where fe(i,j) == + hnam := INTERN STRCONC ('"h",STRINGIMAGE i,STRINGIMAGE j) + [['bcStrings,[6, "0.0", hnam, 'F]]] + prefix := ('"\newline ") + labelList := [['text,:prefix],:labelList] + hList := [['text,:middle],:hList] + equationPart := [ + '(domainConditions + (isDomain EM $EmptyMode) + (isDomain S (String)) + (isDomain F (Float)) + (isDomain I (Integer))), + :xpList,:cList,:ylList,:yrList,:hList] + page := htInitPage('"D02KEF - 2nd order Sturm-Liouville problem, regular/singular system, finite/infinite range, eigenvalue and eigenfunction, user-specified break-points", nil) + htSay '"\menuitemstyle{}\tab{2} Enter points where boundary " + htSay '"conditions are to be imposed {\it xpoint}: \newline " + htMakePage equationPart + htMakeDoneButton('"Continue",'d02kefGen) + htpSetProperty(page,'m,m) + htpSetProperty(page,'match,match) + htpSetProperty(page,'k,k) + htpSetProperty(page,'tol,tol) + htpSetProperty(page,'elam,elam) + htpSetProperty(page,'delam,delam) + htpSetProperty(page,'maxit,maxit) + htpSetProperty(page,'maxfun,maxfun) + htpSetProperty(page,'ifail,ifail) + htpSetProperty(page,'inputArea, htpInputAreaAlist htPage) + htShowPage() + +d02kefDefaultSolve(htPage,match,k,tol,elam,delam,maxit,maxfun,ifail) == + m := '5 + page := htInitPage('"D02KEF - 2nd order Sturm-Liouville problem, regular/singular system, finite/infinite range, eigenvalue and eigenfunction, user-specified break-points", nil) + htMakePage '( + (domainConditions + (isDomain EM $EmptyMode) + (isDomain F (Float)) + (isDomain I (Integer))) + (text . "\newline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Enter points where boundary conditions are to be imposed ") + (text . "{\it xpoint}: \newline ") + (bcStrings (10 "0.0" xp1 F)) + (bcStrings (10 "0.1" xp2 F)) + (bcStrings (10 "4**(1/3)" xp3 F)) + (bcStrings (10 "30.0" xp4 F)) + (bcStrings (10 "30.0" xp5 F)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Value of {\it p} for COEFFN: \newline ") + (bcStrings (42 "1.0" c1 EM)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Value of {\it q} for COEFFN: \newline ") + (bcStrings (42 "ELAM-X-2.0/(X*X)" c2 EM)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Value of {\it dqdl} for COEFFN: \newline ") + (bcStrings (42 "1.0" c3 EM)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Values of YL(1) & YL(2) for BDYVAL: \newline ") + (bcStrings (42 "XL" yl1 EM)) + (bcStrings (42 "2.0" yl2 EM)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Values of YR(1) & YR(2) for BDYVAL: \newline ") + (bcStrings (42 "1.0" yr1 EM)) + (bcStrings (42 "-sqrt(XR-ELAM)" yr2 EM)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Maximum step size {\it hmax(2,m)}: \newline ") + (bcStrings (6 "0.0" h11 F)) + (bcStrings (6 "0.0" h12 F)) + (bcStrings (6 "0.0" h13 F)) + (bcStrings (6 "0.0" h14 F)) + (bcStrings (6 "0.0" h15 F)) + (text . "\newline ") + (bcStrings (6 "0.0" h21 F)) + (bcStrings (6 "0.0" h22 F)) + (bcStrings (6 "0.0" h23 F)) + (bcStrings (6 "0.0" h24 F)) + (bcStrings (6 "0.0" h25 F))) + htpSetProperty(page,'m,m) + htpSetProperty(page,'match,match) + htpSetProperty(page,'k,k) + htpSetProperty(page,'tol,tol) + htpSetProperty(page,'elam,elam) + htpSetProperty(page,'delam,delam) + htpSetProperty(page,'maxit,maxit) + htpSetProperty(page,'maxfun,maxfun) + htpSetProperty(page,'ifail,ifail) + htMakeDoneButton('"Continue",'d02kefGen) + htpSetProperty(page,'inputArea, htpInputAreaAlist htPage) + htShowPage() + +d02kefGen htPage == + m := htpProperty(htPage, 'm) + match := htpProperty(htPage, 'match) + k := htpProperty(htPage, 'k) + tol := htpProperty(htPage, 'tol) + elam := htpProperty(htPage, 'elam) + delam := htpProperty(htPage, 'delam) + maxit := htpProperty(htPage, 'maxit) + maxfun := htpProperty(htPage, 'maxfun) + ifail := htpProperty(htPage,'ifail) + alist := htpInputAreaAlist htPage + y := alist + for i in 1..m repeat + for j in 1..2 repeat + h := STRCONC((first y).1," ") + rowList := [h,:rowList] + y := rest y + hList := [:hList,rowList] + rowList := [] + hList := reverse hList + hstring := bcwords2liststring [bcwords2liststring x for x in hList] + for i in 1..2 repeat + for j in 1..2 repeat + b := STRCONC((first y).1," ") + rowList := [b,:rowList] + y := rest y + bList := [:bList,rowList] + rowList := [] + bList := reverse bList + bstring := bcwords2liststring [bcwords2liststring x for x in bList] + for i in 1..3 repeat + c := STRCONC((first y).1," ") + cList := [c,:cList] + y := rest y + cstring := bcwords2liststring cList + while y repeat + x := STRCONC((first y).1," ") + xList := [x,:xList] + y := rest y + xstring := bcwords2liststring xList + prefix := STRCONC("d02kef([",xstring,"]::Matrix DoubleFloat, ",STRINGIMAGE m) + prefix := STRCONC(prefix,", ",STRINGIMAGE k,", ",tol,", ",STRINGIMAGE maxfun) + prefix := STRCONC(prefix,", ",STRINGIMAGE match,", ",STRINGIMAGE elam,", ") + prefix:=STRCONC(prefix,STRINGIMAGE delam,", ",hstring,", ",STRINGIMAGE maxit) + end := STRCONC(", ",STRINGIMAGE ifail,",(",cstring,"::Vector(Expression Float))::ASP10(COEFFN)") + end := STRCONC(end,", (",bstring,"::Matrix Expression Float)::ASP80('BDYVAL))") + linkGen STRCONC (prefix,end) + +d02raf() == + htInitPage('"D02RAF - ODEs, general nonlinear boundary value problem, finite difference technique with deferred correction, continuation facility",nil) + htMakePage '( + (domainConditions + (isDomain PI (PositiveInteger))) + (text . "\windowlink{Manual Page}{manpageXXd02raf} for this routine ") + (text . "\newline ") + (text . "\lispwindowlink{Browser operation page}{(|oPageFrom| '|d02raf| '|NagOrdinaryDifferentialEquationsPackage|)} for this routine") + (text . "\newline \horizontalline ") + (text . "\newline ") + (text . "D02RAF solves a two-point boundary value problem for a system ") + (text . "of {\it n} first-order ordinary differential equations ") + (text . "{\it \htbitmap{yi}'= \htbitmap{fi}(x,y)}, for {\it i} = 1,2,...,") + (text . "{\it n}, on the range [a,b] with {\it n} nonlinear boundary ") + (text . "conditions \htbitmap{gi}{\it (y(a),y(b)) = 0} for {\it i} = 1,2,") + (text . "...,{\it n} using a deferred correction technique and a Newton ") + (text . "iteration; the solution is computed on a mesh. A continuation ") + (text . "facility is provided for which a family of problems is solved ") + (text . "posed as {\it y' = f(x,y,\epsilon)} subject to the boundary ") + (text . "conditions {\it g(y(a),y(b),\epsilon) = 0}, where \epsilon ") + (text . "is the continuation parameter. The choice \epsilon = 0 should ") + (text . "define an easy problem to solve and \epsilon = 1 the problem ") + (text . "whose solution is required; a sequence of problems is solved ") + (text . "with 0 = \htbitmap{ep1} < \htbitmap{ep2} < ... \htbitmap{epp} ") + (text . "= 1 where {\it p} and the \htbitmap{epi} are chosen by D02RAF. ") + (text . "\blankline ") + (text . "\newline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Enter the number of differential equations {\it n}: ") + (text . "\newline\tab{2} ") + (bcStrings (5 3 n PI)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "The maximum number of points in the mesh {\it mnp}: ") + (text . "\newline\tab{2} ") + (bcStrings (5 40 mnp PI)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Number of points in the initial mesh {\it np}:") + (text . "\newline\tab{2} ") + (bcStrings (5 17 np PI)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "\newline Number of boundary conditions involving y(a) only ") + (text . "{\it numbeg}: \newline\tab{2} ") + (bcStrings (5 2 numbeg PI)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "\newline Boundary conditions involving both y(a) and ") + (text . "y(b) {\it nummix}: \newline\tab{2} ") + (text . "\newline\tab{2} ") + (bcStrings (5 0 nummix PI)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Absolute error tolerance {\it tol}: ") + (text . "\newline\tab{2} ") + (bcStrings (10 "1.0e-4" tol F)) + (text . "\blankline ") + (text . "\newline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Do you wish to use an intial mesh or default values,{\it init} ") + (radioButtons init + ("" " default values" init_zero) + ("" " initial mesh" init_nonZero)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "First dimension of y, {\it iy}: ") + (text . "\newline\tab{2} ") + (bcStrings (5 3 iy PI)) + (text . "\blankline ") + (text . "\newline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Are JACOBF & JACOBG routines being supplied, {\it ijac}:") + (radioButtons ijac + ("" " yes" ijac_nonZero) + ("" " no" ijac_zero)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Continuation facility {\it deleps}:") + (text . "\newline\tab{2} ") + (bcStrings (5 "0.1" deleps F)) + (text . "\newline\tab{2} ") + (text . "Note: For 0.0 \htbitmap{great=} deleps > 1.0, continuation ") + (text . "is not used. ") + (text . "\blankline ") + (text . "\newline \tab{2} ") + (text . "Ifail is input in three components: ") + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "{\it a} ") + (radioButtons afail + ("" " 0, hard failure" azero) + ("" " 1, soft failure" aone)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "{\it b} ") + (radioButtons bfail + ("" " 1, print error messages" bone) + ("" " 0, suppress error messages" bzero)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "{\it c} ") + (radioButtons cfail + ("" " 1, print warning messages" cone) + ("" " 0, suppress warning messages" czero))) + htMakeDoneButton('"Continue", 'd02rafSolve) + htShowPage() + +d02rafSolve htPage == + n := + $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'n) + objValUnwrap htpLabelSpadValue(htPage, 'n) + mnp := + $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'mnp) + objValUnwrap htpLabelSpadValue(htPage, 'mnp) + np := + $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'np) + objValUnwrap htpLabelSpadValue(htPage, 'np) + numbeg := + $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'numbeg) + objValUnwrap htpLabelSpadValue(htPage, 'numbeg) + nummix := + $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'nummix) + objValUnwrap htpLabelSpadValue(htPage, 'nummix) + tol := htpLabelInputString(htPage,'tol) + mesh := htpButtonValue(htPage,'init) + init := + mesh = 'init_zero => '0 + '1 + iy := + $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'iy) + objValUnwrap htpLabelSpadValue(htPage, 'iy) + jacob := htpButtonValue(htPage,'ijac) + ijac := + jacob = 'ijac_zero => '0 + '1 + deleps := htpLabelInputString(htPage,'deleps) + lwork := mnp*(3*n*n + 6*n +2) +4*n*n + 3*n + liwork := + ijac = 0 => mnp*(2*n +1) + n*n + 4*n +2 + mnp*(2*n +1) + n + aerror := htpButtonValue(htPage,'afail) + afail := + aerror = 'azero => '0 + '1 + berror := htpButtonValue(htPage,'bfail) + bfail := + berror = 'bone => '1 + '0 + cerror := htpButtonValue(htPage,'cfail) + cfail := + cerror = 'cone => '1 + '0 + ifail := 100*cfail + 10*bfail + afail + (n = '3 and init = '0 and iy = '3 and nummix = '0 and numbeg = '2 and np = '17 and mnp = '40) => d02rafDefaultSolve(htPage,mnp,np,numbeg,nummix,tol,init,iy,ijac,deleps,lwork,liwork,ifail) + init = '1 => d02rafCopOut() + funcList := + "append"/[fa(i) for i in 1..n] where fa(i) == + prefix := ('"\newline {\em Function f") + prefix := STRCONC(prefix,STRINGIMAGE i,'":} \space{1}") + funct := STRCONC ('"Y[",STRINGIMAGE i ,"]") + fnam := INTERN STRCONC ('"f",STRINGIMAGE i) + [['text,:prefix],['bcStrings,[42, funct, fnam, 'EM]]] + middle := ('"\blankline \menuitemstyle{} \tab{2} Enter the functions ") + middle := STRCONC(middle,'"\htbitmap{gi} below ") + middle := STRCONC(middle,'"as functions of YA[i] and YB[i]: \newline ") + gList := + "append"/[fb(i) for i in 1..n] where fb(i) == + prefix := ('"\newline {\em Function g") + prefix := STRCONC(prefix,STRINGIMAGE i,'":} \space{1}") + fnc := STRCONC ('"YA[",STRINGIMAGE i ,"]") + gnam := INTERN STRCONC ('"g",STRINGIMAGE i) + [['text,:prefix],['bcStrings,[42, fnc, gnam, 'EM]]] + gList := [['text,:middle],:gList] + mid:= ('"\blankline \menuitemstyle{} \tab{2} Enter the array ") + mid := STRCONC(mid,'"{\it x(mnp)}: \newline ") + xList := + "append"/[fc(i) for i in 1..mnp] where fc(i) == + xnam := INTERN STRCONC ('"x",STRINGIMAGE i) + [['bcStrings,[4, 0, xnam, 'F]]] + xList := [['text,:mid],:xList] + equationPart := [ + '(domainConditions + (isDomain EM $EmptyMode) + (isDomain S (String)) + (isDomain F (Float)) + (isDomain I (Integer))), + :funcList,:gList,:xList] + page := htInitPage('"D02RAF - ODEs, general nonlinear boundary value problem, finite difference technique with deferred correction, continuation facility",nil) + htSay '"\menuitemstyle{}\tab{2} " + htSay '"Enter the functions \htbitmap{fi} (i.e. the derivatives) below " + htSay '"as functions of Y[1]...Y[n]: " + htSay '"\newline " + htMakePage equationPart + htMakeDoneButton('"Continue",'d02rafGen) + htpSetProperty(page,'n,n) + htpSetProperty(page,'mnp,mnp) + htpSetProperty(page,'np,np) + htpSetProperty(page,'numbeg,numbeg) + htpSetProperty(page,'nummix,nummix) + htpSetProperty(page,'tol,tol) + htpSetProperty(page,'init,init) + htpSetProperty(page,'iy,iy) + htpSetProperty(page,'ijac,ijac) + htpSetProperty(page,'deleps,deleps) + htpSetProperty(page,'lwork,lwork) + htpSetProperty(page,'liwork,liwork) + htpSetProperty(page,'ifail,ifail) + htpSetProperty(page,'inputArea, htpInputAreaAlist htPage) + htShowPage() + + +d02rafDefaultSolve(htPage,mnp,np,numbeg,nummix,tol,init,iy,ijac,deleps,lwork,liwork,ifail) == + n := '3 + page := htInitPage('"D02RAF - ODEs, general nonlinear boundary value problem, finite difference technique with deferred correction, continuation facility",nil) + htMakePage '( + (domainConditions + (isDomain EM $EmptyMode) + (isDomain F (Float)) + (isDomain I (Integer))) + (text . "\newline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Enter the functions \htbitmap{fi} (i.e. the derivatives) below ") + (text . "as functions of Y[1]...Y[n]: ") + (text . "\newline {\em Function f1:} \space{1}") + (bcStrings (44 "Y[2]" f1 EM)) + (text . "\newline {\em Function f2:} \space{1}") + (bcStrings (44 "Y[3]" f2 EM)) + (text . "\newline {\em Function f3:} \space{1}") + (bcStrings (44 "-Y[1]*Y[3] - 2*EPS*(1-Y[2]*Y[2])" f3 EM)) + (text . "\blankline ") + (text . "\newline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Enter the functions \htbitmap{gi} below ") + (text . "as functions of YA[i] and YB[i]: ") + (text . "\newline {\em Function g1:} \space{1}") + (bcStrings (44 "YA[1]" g1 EM)) + (text . "\newline {\em Function g2:} \space{1}") + (bcStrings (44 "YA[2]" g2 EM)) + (text . "\newline {\em Function g3:} \space{1}") + (bcStrings (44 "YB[2] -1" g3 EM)) + (text . "\blankline ") + (text . "\newline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Enter the array {\it x(mnp)}: \newline ") + (bcStrings (4 "0.0" x1 F)) + (bcStrings (4 "0.0" x2 F)) + (bcStrings (4 "0.0" x3 F)) + (bcStrings (4 "0.0" x4 F)) + (bcStrings (4 "0.0" x5 F)) + (bcStrings (4 "0.0" x6 F)) + (bcStrings (4 "0.0" x7 F)) + (bcStrings (4 "0.0" x8 F)) + (bcStrings (4 "0.0" x9 F)) + (bcStrings (4 "0.0" x10 F)) + (bcStrings (4 "0.0" x11 F)) + (bcStrings (4 "0.0" x12 F)) + (bcStrings (4 "0.0" x13 F)) + (bcStrings (4 "0.0" x14 F)) + (bcStrings (4 "0.0" x15 F)) + (bcStrings (4 "0.0" x16 F)) + (bcStrings (4 "10.0" x17 F)) + (bcStrings (4 "0.0" x18 F)) + (bcStrings (4 "0.0" x19 F)) + (bcStrings (4 "0.0" x20 F)) + (bcStrings (4 "0.0" x21 F)) + (bcStrings (4 "0.0" x22 F)) + (bcStrings (4 "0.0" x23 F)) + (bcStrings (4 "0.0" x24 F)) + (bcStrings (4 "0.0" x25 F)) + (bcStrings (4 "0.0" x26 F)) + (bcStrings (4 "0.0" x27 F)) + (bcStrings (4 "0.0" x28 F)) + (bcStrings (4 "0.0" x29 F)) + (bcStrings (4 "0.0" x30 F)) + (bcStrings (4 "0.0" x31 F)) + (bcStrings (4 "0.0" x32 F)) + (bcStrings (4 "0.0" x33 F)) + (bcStrings (4 "0.0" x34 F)) + (bcStrings (4 "0.0" x35 F)) + (bcStrings (4 "0.0" x36 F)) + (bcStrings (4 "0.0" x37 F)) + (bcStrings (4 "0.0" x38 F)) + (bcStrings (4 "0.0" x39 F)) + (bcStrings (4 "0.0" x40 F))) + htpSetProperty(page,'n,n) + htpSetProperty(page,'mnp,mnp) + htpSetProperty(page,'np,np) + htpSetProperty(page,'numbeg,numbeg) + htpSetProperty(page,'nummix,nummix) + htpSetProperty(page,'tol,tol) + htpSetProperty(page,'init,init) + htpSetProperty(page,'iy,iy) + htpSetProperty(page,'ijac,ijac) + htpSetProperty(page,'deleps,deleps) + htpSetProperty(page,'lwork,lwork) + htpSetProperty(page,'liwork,liwork) + htpSetProperty(page,'ifail,ifail) + htMakeDoneButton('"Continue",'d02rafGen) + htpSetProperty(page,'inputArea, htpInputAreaAlist htPage) + htShowPage() + +d02rafGen htPage == + n := htpProperty(htPage, 'n) + mnp := htpProperty(htPage, 'mnp) + np := htpProperty(htPage, 'np) + numbeg := htpProperty(htPage, 'numbeg) + nummix := htpProperty(htPage, 'nummix) + tol := htpProperty(htPage, 'tol) + init := htpProperty(htPage, 'init) + iy := htpProperty(htPage, 'iy) + ijac := htpProperty(htPage, 'ijac) + deleps := htpProperty(htPage, 'deleps) + lwork := htpProperty(htPage, 'lwork) + liwork := htpProperty(htPage, 'liwork) + ifail := htpProperty(htPage, 'ifail) + alist := htpInputAreaAlist htPage + y := alist + for i in 1..mnp repeat + xtemp := STRCONC((first y).1," ") + xList := [xtemp,:xList] + y := rest y + xstring := bcwords2liststring xList + for i in 1..n repeat + gtemp := STRCONC((first y).1," ") + gList := [gtemp,:gList] + y := rest y + gstring := bcwords2liststring gList + while y repeat + f := STRCONC((first y).1," ") + fList := [f,:fList] + y := rest y + fstring := bcwords2liststring fList + prefix := STRCONC("d02raf(",STRINGIMAGE n,", ",STRINGIMAGE mnp,", ") + prefix := STRCONC(prefix,STRINGIMAGE numbeg,", ",STRINGIMAGE nummix,", ") + prefix := STRCONC(prefix,tol,", ",STRINGIMAGE init,", ",STRINGIMAGE iy,", ") + middle:= STRCONC(STRINGIMAGE ijac,", ",STRINGIMAGE lwork,", ") + middle := STRCONC(middle,STRINGIMAGE liwork,", ",STRINGIMAGE np,", [") + middle := STRCONC(middle,xstring,"],[[0.0 for i in 1..", STRINGIMAGE mnp) + middle := STRCONC(middle,"] for j in 1..",STRINGIMAGE iy,"]") + middle := STRCONC(middle,":: Matrix DoubleFloat,",STRINGIMAGE deleps,", ") + middle := STRCONC(middle,STRINGIMAGE ifail,", (",fstring,"::Vector ") + middle := STRCONC(middle,"Expression Float)::ASP41('FCN,'JACOBF,'JACEPS),(") + middle := STRCONC(middle,gstring,"::Vector Expression Float)::ASP42('G,'JACOBG,") + middle := STRCONC(middle,"'JACGEP))") + linkGen STRCONC(prefix,middle) + + +d02rafCopOut() == + htInitPage('"D02RAF - ODEs, general nonlinear boundary value problem, finite difference technique with deferred correction, continuation facility",nil) + htMakePage '( + (domainConditions + (isDomain PI (PositiveInteger))) + (text . "\blankline ") + (text . "{\center{\em Hyperdoc interface not available for initial mesh}}") + (text . "\newline ") + (text . "{\center{\em Please use the command line.}}")) + htMakeDoneButton('"Continue",'d02raf) + htShowPage() +@ +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} |