John Cagnol


Paris, France

Introduction au Calcul Scientifique
ESI CS 1402 - Printemps 2010

Simulations faites avec Maple dans le chapitre II, Paragraphe II

> with(DEtools):
equation1 := diff(N(t),t) = 4*N(t)-2*N(t)*P(t);
equation2 := diff(P(t),t) = -3*P(t)+N(t)*P(t);
diff(N(t), t) = `+`(`*`(4, `*`(N(t))), `-`(`*`(2, `*`(N(t), `*`(P(t))))))
diff(P(t), t) = `+`(`-`(`*`(3, `*`(P(t)))), `*`(N(t), `*`(P(t))))
> DEplot({equation1, equation2}, {N(t), P(t)}, t = 0 .. 2, N = 0 .. 8, P = 0 .. 5, [[N(0) = 1, P(0) = 1]], stepsize = 0.1e-2, numpoints = 7009, animatecurves = true);
Plot_2d
> DEplot({equation1, equation2}, {N(t), P(t)}, t = 0 .. 7, [[N(0) = 1, P(0) = 1]], scene=[t,N(t)], stepsize = 0.1e-2, numpoints = 7009, animatecurves = true, linecolor=red);
Plot_2d
> DEplot({equation1, equation2}, {N(t), P(t)}, t = 0 .. 7, [[N(0) = 1, P(0) = 1]], scene=[t,P(t)], stepsize = 0.1e-2, numpoints = 7009, animatecurves = true);
Plot_2d
> Nplot:=DEplot({equation1, equation2}, {N(t), P(t)}, t = 0 .. 7, [[N(0) = 1, P(0) = 1]], scene=[t,N(t)], stepsize = 0.1e-2, linecolor=red):
Pplot:=DEplot({equation1, equation2}, {N(t), P(t)}, t = 0 .. 7, [[N(0) = 1, P(0) = 1]], scene=[t,P(t)], stepsize = 0.1e-2, linecolor=blue):
plots[display](Nplot,Pplot);
Plot_2d
> DEplot3d({equation1, equation2}, {N(t), P(t)}, t = 0 .. 7, N = 0 .. 8, P = 0 .. 5, [[N(0) = 1, P(0) = 1]], stepsize = 0.1e-2, numpoints = 7009, animatecurves = true);
Plot