clear all
close all
% example 2
% f''-f = -1, f(-1)=0, f(1)=2  % in class the right hand side is +1 but the
% idea to solve the system is the same
N = 50;
X = linspace(-1,1,N+1);
dx = 2/N;

L = diag(-2*ones(1,N+1)) + diag(ones(1,N),1) + diag(ones(1,N),-1);

L(1,1)=1; L(1,2)=0;
L(N+1,N+1)=1; L(N+1,N)=0;

Q = -diag(ones(1,N+1))*dx^2;
Q(1,1)=0;
Q(N+1,N+1)=0;
r = -ones(N+1,1)*dx^2; % use the notation in class (in fact it is the right hand side vector b)
r(1)=0;
r(N+1)=2;
F = (L+Q)\r;
plot(X,F)