function [x,U]=fin_diff_solve(N)

% compute finite difference solution to u''+u=0 on uniform grid
% with u(-1)=u(1)=1
% exact solution is u(x)=cos(x)/cos(1)

% set up uniform grid
h=2/N;
x=-1:h:1; x=x(:);

% set up finite difference matrix
e=ones(N-1,1);
A=spdiags([e -2*e e], -1:1, N-1, N-1);
A=A/h^2;

% set up right-hand-side
b=zeros(N-1,1); b(1)=-1/h^2; b(N-1)=-1/h^2;

% solve linear system
U=(A+speye(N-1))\b;

% add boundary data to U
U=[1;U;1];
err=norm(U-cos(x)/cos(1),Inf)
plot(x,U)