######################################################################################### # # # Gewoehnliche Differentialgleichungen -- Eine Einfuehrung aus der Perspektive der # # Dynamischen Systeme # # # # Vieweg + Teubner, 2009 # # # # # # MAPLE-Beispiele aus Anhang A.4 - Grafische Darstellung der Loesungen # # # # # # (C) Lars Gruene, Oliver Junge 2008 # #########################################################################################

restart;

bsp1 := diff(x(t), t) = x(t)^2;

bsp2 := diff(x1(t),t)=x2(t), diff(x2(t),t)=-x1(t);

ab1num := x(1) = 10;

ab2num := x1(0) = 5, x2(0) = 2;

lsg1:=dsolve({bsp1,ab1num});

xt := rhs(lsg1);

plot(xt,t=-10..1);

lsg2:=dsolve({bsp2,ab2num});

x1t:=rhs(lsg2[1]); x2t:=rhs(lsg2[2]);

plot([x1t, x2t], t=0..10, color=[red, blue], style=[point, line], thickness=[1,2], numpoints=200);

kurve1:=plot(x1t, t=0..10, color=red, style=point, thickness=1, numpoints=200): kurve2:=plot(x2t, t=0..10, color=blue, style=line, thickness=2, numpoints=200): plots[display](kurve1,kurve2);

plot([x1t, x2t, t=0..10]);

plot3d([t,x1t,x2t],t=0..20,x=-1..1,grid=[100,2], axes=boxed,labels=["t","x1","x2"],orientation=[-111,67], thickness=2);

numlsg1:=dsolve({bsp1,ab1num}, numeric, range=-10..1);

with(plots):

odeplot(numlsg1,numpoints=200);

odeplot(numlsg1,numpoints=200,frames=20);

numlsg2:=dsolve({bsp2,ab2num}, numeric, range=0..20);

odeplot(numlsg2,[[t,x1(t),color=blue,style=point],[t,x2(t),color=red,style=line]],0..10,refine=2);

odeplot(numlsg2,[[t,x1(t),color=blue,style=point],[t,x2(t),color=red,style=line]],0..10,numpoints=200);

odeplot(numlsg2,[x1(t),x2(t)],0..7);

odeplot(numlsg2,[t,x1(t),x2(t)],refine=2,axes=boxed,labels=["t","x1","x2"],orientation=[-111,70],thickness=2);