% MATLAB code to solve u"=f(x) using finite differences
clear;clf;
n =5
h=1/n;
x=0:h:1;xf=0:h/20:1;
A=diag(ones(n-2,1),-1)-2*diag(ones(n-1,1),0)+diag(ones(n-2,1),1);
u=h^2*(A\sin(pi*x(2:n)'))
u = [0;u;0];
plot(x,u,'r--o',xf,-sin(pi*xf)/pi^2,'k-','linewidth',2,'markerfacecolor','r')
xlabel('x');
ylabel(' u(x)'); 
title(' Finite difference solution to: D^2 u = f(x) ')
legend(' Finite Difference ',' Exact ',4)