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author | dos-reis <gdr@axiomatics.org> | 2007-08-14 05:14:52 +0000 |
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committer | dos-reis <gdr@axiomatics.org> | 2007-08-14 05:14:52 +0000 |
commit | ab8cc85adde879fb963c94d15675783f2cf4b183 (patch) | |
tree | c202482327f474583b750b2c45dedfc4e4312b1d /src/input/zimmer.input.pamphlet | |
download | open-axiom-ab8cc85adde879fb963c94d15675783f2cf4b183.tar.gz |
Initial population.
Diffstat (limited to 'src/input/zimmer.input.pamphlet')
-rw-r--r-- | src/input/zimmer.input.pamphlet | 393 |
1 files changed, 393 insertions, 0 deletions
diff --git a/src/input/zimmer.input.pamphlet b/src/input/zimmer.input.pamphlet new file mode 100644 index 00000000..3cfc0661 --- /dev/null +++ b/src/input/zimmer.input.pamphlet @@ -0,0 +1,393 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input zimmer.input} +\author{The Axiom Team} +\maketitle +\begin{abstract} +These examples come from Postel & Zimmermann's paper in the 5th Rhine +Conference on Computer Algebra. +\end{abstract} +\eject +\tableofcontents +\eject +\section{License} +<<license>>= +--Copyright The Numerical Algorithms Group Limited 1996. +@ +<<*>>= +<<license>> +)set break resume + +-- First Order Equations + +-- 1 + +u := operator 'u +ode := (x^4-x^3)*D(u x,x) + 2*x^4*u(x) = x^3/3 + C +solve(ode,u,x) + +-- 2 +)clear all + +u := operator 'u +ode := -D(u x,x)/2 + u(x) = sin(x) +solve(ode,u,x) + +-- 3 +)clear all + +y := operator 'y +ode := D(y x,x) = y(x)/(y(x)*log(y(x)) + x) +solve(ode,y,x) + +-- 4 +)clear all + +y := operator 'y +ode := 2*y(x)*D(y x,x)^2 -2*x*D(y x,x)-y(x) = 0 +solve(ode,y,x) + +-- 5 +)clear all + +y := operator 'y +ode := D(y x,x) + y(x) = y(x)^3*sin(x) +solve(ode,y,x) + +-- 6 +)clear all + +y := operator 'y +P := operator 'P +Q := operator 'Q +ode := D(y x,x) + P(x)*y(x) = Q(x)*y(x)^n +solve(ode,y,x) +solve(eval(ode,n=1),y,x) +solve(eval(ode,n=2),y,x) +solve(eval(ode,n=%pi),y,x) +solve(eval(ode,n=%e),y,x) +solve(eval(ode,n=sqrt(2)),y,x) + +-- 7 +)clear all + +y := operator 'y +ode := (x^2-1)*D(y x,x)^2 - 2*x*y(x)*D(y x,x)+(y x)^2 - 1 = 0 +solve(ode,y,x) + +-- 8 +)clear all + +y := operator 'y +f := operator 'f +g := operator 'g +ode := f(x*D(y x,x) - y(x)) = g(D(y x,x)) +solve(ode,y,x) + +-- 9 +)clear all + +y := operator 'y +ode := D(y x,x) = (3*x^2-y(x)^2-7)/(exp(y(x))+2*x*y(x)+1) +solve(ode,y,x) + +-- 10 +)clear all + +y := operator 'y +ode := D(y x,x) = (2*x^3*y(x) - (y x)^4)/(x^4 - 2*x*(y x)^3) +solve(ode,y,x) + +-- 11 +)clear all + +y := operator 'y +ode := D(y x,x)*(D(y x,x) + y(x)) = x*(x + y(x)) +solve(ode,y,x) + +-- 12 +)clear all + +y := operator 'y +ode := D(y x,x) = x/(x^2*(y x)^2 + (y x)^5) +solve(ode,y,x) + +-- 13 +)clear all + +y := operator 'y +ode := y(x) = 2*x*D(y x,x) - a*D(y x,x)^3 +solve(ode,y,x) + +-- 14 +)clear all + +y := operator 'y +ode := y(x) = 2*x*D(y x,x) - D(y x,x)^3 +solve(ode,y,x) + +-- 15 +)clear all + +y := operator 'y +ode := D(y x,x) = exp(x)*(y x)^2 - y(x) + exp(-x) +solve(ode,y,x) + +-- 16 +)clear all + +y := operator 'y +ode := D(y x,x) = (y x)^2 - x*y(x) + 1 +solve(ode,y,x) + +-- 17 +)clear all + +y := operator 'y +ode := D(y x,x) = (9*x^8 + 1)/((y x)^2 +1) +solve(ode,y,x) + +-- 18 +)clear all + +y := operator 'y +ode := y(x)=2*x*D(y x,x) + y(x)*D(y x,x)^2 +solve(ode,y,x) + +-- 19 +)clear all +y := operator 'y +ode := x = y(x)*D(y x,x) - x*D(y x,x)^2 +solve(ode,y,x) + +-- Second Order Equations + +-- 20 +)clear all +y := operator 'y +ode := D(y x,x,2)*(a*x+b)^2+4*D(y x,x)*(a*x+b)*a+2*y(x)*a^2=0 +solve(ode,y,x) + +-- 21 +)clear all +u := operator 'u +ode := (x^2 - x)*D(u x,x,2) + (2*x^2+4*x-3)*D(u x,x) + 8*x*u(x)=1 +solve(ode,u,x) + +-- 22 +)clear all +w := operator 'w +ode := (x^2 - x)*D(w x,x,2) + (1-2*x^2)*D(w x,x) + (4*x - 2)*w(x) = 0 +solve(ode,w,x) + +-- 23 +)clear all +y := operator 'y +ode := D(y x,x,2) - D(y x,x) = 2*y(x)*D(y x,x) +solve(ode,y,x) + +-- 24 +)clear all +y := operator 'y +ode := D(y x,x,2)/y(x) - D(y x,x)^2/y(x)^2 -1 + y(x)^(-3) = 0 +solve(ode,y,x) + +-- 25 +)clear all +y := operator 'y +ode := D(y x,x,2) + 2*x*D(y x,x) = 2*x +solve(ode,y,x) + +-- 26 +)clear all +y := operator 'y +ode := 2*y(x)*D(y x,x,2) - D(y x,x)^2 = (D(y x,x) - x*D(y x,x,2))^2/3 +solve(ode,y,x) + +-- 27 +)clear all +y := operator 'y +ode := x*D(y x,x,2) = 2*y(x)*D(y x,x) +solve(ode,y,x) + +-- 28 +)clear all +y := operator 'y +ode := (1-x)*(y(x)*D(y x,x,2) - D(y x,x)^2) + x^2*y(x)^2 = 0 +solve(ode,y,x) + +-- 29 +)clear all +y := operator 'y +ode := x*y(x)*D(y x,x,2) + x*D(y x,x)^2 + y(x)*D(y x,x) = 0 +solve(ode,y,x) + +-- 30 +)clear all +y := operator 'y +ode := D(y x,x,2)^2 - 2*D(y x,x,2)*D(y x,x) + 2*y(x)*D(y x,x) -y(x)^2 = 0 +solve(ode,y,x) + +-- 31 +)clear all +y := operator 'y +ode := (x^3/2-x^2)*D(y x,x,2) + (2*x^2-3*x+1)*D(y x,x) + (x-1)*y(x) = 0 +solve(ode,y,x) + +-- 32 +)clear all +y := operator 'y +ode := D(y x,x,2) - 2*x*D(y x,x) + 2*y(x) = 3 +solve(ode,y,x) + +-- 33 +)clear all +y := operator 'y +ode := sqrt(x)*D(y x,x,2) + 2*x*D(y x,x) + 3*y(x) = 0 +solve(ode,y,x) + +-- 34 +)clear all +y := operator 'y +ode := x^2*D(y x,x,2) + 3*x*D(y x,x) = 1/(x^4*y(x)^3) +solve(ode,y,x) + +-- 35 +)clear all +y := operator 'y +ode := D(y x,x,2) - 2/x^2*y(x) = 7*x^4 +3*x^3 +solve(ode,y,x) + +-- 36 +)clear all +y := operator 'y +ode := D(y x,x,2) +y(x) = csc(x) +solve(ode,y,x) + +-- Higher Order Equations + +-- 37 +)clear all +y := operator 'y +ode := D(y x,x,7) - 14*D(y x,x,6) +80*D(y x,x,5) -242*D(y x,x,4) + _ + 419*D(y x,x,3) - 416*D(y x,x,2) +220*D(y x,x) -48*y(x) = 0 +solve(ode,y,x) + +-- 38 +)clear all +y := operator 'y +ode := D(y x,x,4) -4/x^2*D(y x,x,2) + 8/x^3*D(y x,x) -8/x^4*D(y x,x) = 0 +solve(ode,y,x) + +-- 39 +)clear all +y := operator 'y +ode := (1+x+x^2)*D(y x,x,3) + (3+6*x)*D(y x,x,2) +6*D(y x,x) = 6*x +solve(ode,y,x) + +-- 40 +)clear all +y := operator 'y +ode := (D(y x,x)^2 +1)*D(y x,x,3) - 3*D(y x,x)*D(y x,x,2) = 0 +solve(ode,y,x) + +-- 41 +)clear all +y := operator 'y +ode := 3*D(y x,x,2)*D(y x,x,4) - 5*D(y x,x,3)^2 = 0 +solve(ode,y,x) + +-- Special Equations + +-- 42 +)clear all +y := operator 'y +ode := D(y t,t) + a*y(t-1) = 0 +solve(ode,y,t) + +-- 43 +)clear all +y := operator 'y +ode := D(y(x,a),x) = a*y(x,a) +solve(ode,y,x) + +-- 44 +)clear all +y := operator 'y +ode := D(y x,x,4) = sin(x) +solve(ode,y,x=0,[0,0,0,0]) + +-- 45 +)clear all +y := operator 'y +ode := x*D(y x,x,2) + D(y x,x) +2*x*y(x) =0 +solve(ode,y,x=0,[1,0]) + +-- 46 +)clear all +y := operator 'y +ode := x*D(y x,x)^2 -(y x)^2 + 1 = 0 +solve(ode,y,x=0,[1]) + +-- 47 +)clear all +y := operator 'y +ode := D(y x,x,2) + y(x)*D(y x,x)^3 = 0 +solve(ode,y,x=0,[0,2]) + +-- Systems Of equations + +-- 48 +)clear all +x := operator 'x +y := operator 'y +z := operator 'z +odes := [D(x t,t) = -3*y(t)*z(t), D(y t,t) = 3*x(t)*z(t), D(z t,t) = -x(t)*y(t)] +solve(odes,[x,y,z],t) + +-- 49 +)clear all +x := operator 'x +y := operator 'y +a := operator 'a +b := operator 'b +odes := [D(x t,t) = a(t)*((y t)^2 - (x t)^2) + 2*b(t)*x(t)*y(t) + 2*c*x(t), + D(y t,t) = b(t)*((y t)^2 - (x t)^2) - 2*a(t)*x(t)*y(t) + 2*c*y(t)] +solve(odes,[x,y],t) + +-- 50 +)clear all +x := operator 'x +y := operator 'y +odes := [D(x t,t) = x(t)*(1+cos(t)/(2+sin(t))), D(y t,t) = x(t) - y(t)] +solve(odes,[x,y],t) + +-- 51 +)clear all +x := operator 'x +y := operator 'y +odes := [D(x t,t) = 9*x(t) + 2*y(t), D(y t,t) = x(t) + 8*y(t)] +solve(odes,[x,y],t) + +-- 52 +)clear all +x := operator 'x +y := operator 'y +odes := [D(x t,t) - x(t) - 2*y(t) = 0, D(x t,t,2) - 2*D(y t,t) = 2*t - cos(2*t)] +solve(odes,[x,y],t) + +-- 53 +)clear all +y1 := operator 'y1 +y2 := operator 'y2 +odes := [D(y1 x,x) = -1/(x*(x^2 + 1))*y1(x) + 1/(x^2*(x^2 + 1))*y2(x)+1/x, + D(y2 x,x) = -x^2/(x^2 + 1)*y1(x) + (2*x^2+1)/x/(x^2+1)*y2(x)+1] +solve(odes,[y1,y2],x) + +@ +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} |