> #sfb for cal2 -- 6 Nov 2001
> nextpoint:=proc(f,current,delta)
> local oldx, oldy, newx, newy;
> oldx:=current[1];
> oldy:=current[2];
> newx:=oldx+delta;
> newy:=oldy+eval(f,{x=oldx,y=oldy})*delta;
> return [newx,newy];
> end;
> eulermethod:=proc(f,initial,delta,n)
> local path, current, i;
> path:=[initial]; current:=initial;
> for i from 1 to n do
> current:=nextpoint(f,current,delta);
> path:=[op(path),current];
> od;
> return path;
> end;
> a:=eulermethod(2*y,[0,1],0.1,10);
> with(plots):with(DEtools):
> A:=plot(a,color=red):B:=plot(exp(2*x),x=0..1,color=blue):display(A,B);
> #Hmm... C:=fieldplot([1,2*y],x=0..1,y=-1..6,arrows=LINE):display(A,B,C);
> E:=dfieldplot(diff(y(x),x)=2*y,y(x),x=0..1,y=-1..6,arrows=LINE,color=green):
> display(C,E);
> display(A,B,E);
> a2:=eulermethod(2*y,[0,1],0.01,100):
> A2:=plot(a2,color=black):
> display(A,A2,B,E);
> E2:=dfieldplot(diff(y(x),x)=2*y,y(x),x=0..1,y=-1..6,arrows=LARGE,color=green):
> display(A,A2,B,E2);
> E:=dfieldplot(diff(y(x),x)=y(x)*(4-y(x)),y(x),x=0..4,y=-1..5,arrows=LINE,color=green):
> display(E);
> a:=eulermethod(y*(4-y),[0,1],0.1,40);a2:=eulermethod(y*(4-y),[0,1],0.01,400):
> A2:=plot(a2,color=black):display(A,A2,E);
> a3:=eulermethod(y*(4-y),[0,5],0.1,40);
> a4:=eulermethod(y*(4-y),[0,-1],0.1,40);
> A3:=plot(a3,color=red):A4:=plot(a4,color=red):display(A,A3,A4,E);
>