function [unew]=GS(n,h,u,b)
% this function updates u by unew using GS method.

u(1)=u(2)/2-h^2*b(1)/2;
for j=2:n-2,
    u(j)=(u(j-1)+u(j+1))/2-h^2*b(j)/2;
end
u(n-1)=u(n-2)/2-h^2*b(n-1)/2;

unew=u;