Example
> f:=(t,y)->t+t^2+exp(y);
> w[0]:=1.;h:=0.1;t[0]:=0.;
> for i from 0 to 4 do t[i+1]:=t[i]+h: w[i+1]:=w[i]+h*f(t[i],w[i]): print(t[i+1],w[i+1]); od:
> h:=0.01;for i from 0 to 49 do t[i+1]:=t[i]+h: w[i+1]:=w[i]+h*f(t[i],w[i]): od:
Error, (in evalf/exp/general) argument too large
> for i from 9 by 10 to 49 do print(t[i+1],w[i+1]) od;
Here,
does not satisfy a Lipschitz condition and therefore, we do not have a well-posed problem!
>