This question is related with this other question: Trying to model a simple second order ODE.
On this other question, I get some useful comments on why the simulations are so terrible.
However, I have another question: Why time-step smaller is not better? Thank you in advance.
h=0.05 %h=0.5; max=100; np=max/h; u=; y=; u(1)=0; u(2)=-h^2/2-h; y(1)=0; y(2)=-h^2/2-h; x=[0:h:max]; for i=3:np+1; u(i)=u(i-1)*(h+2)+u(i-2)*(-h-1)+h^2*x(i); y(i)=-(x(i))^2/2-(x(i)); end close all plot(x,u) hold on plot(x,y,'r')