function exercise7task1

w = @(x) 1+sin(4*pi*x);
T = 1;
K = 0.1;

u_a = 0;
u_b = 0;


N = 2^12-1;
h = 1/(N+1);
x = linspace(0,1,N+2);
A = diag(2*ones(N,1)) - diag(ones(N-1,1),1) - diag(ones(N-1,1),-1) + h^2*K/T*eye(N);

right = h^2*w(x(2:end-1))';
right(1) = right(1) + u_a;
right(end) = right(end) + u_b;

u_ref = [u_a;(A\right);u_b];


err = [];
for k = 3:11
    N = 2^k-1;
    h = 1/(N+1);
    x = linspace(0,1,N+2);
    A = diag(2*ones(N,1)) - diag(ones(N-1,1),1) - diag(ones(N-1,1),-1) + h^2*K/T*eye(N);

    right = h^2*w(x(2:end-1))';
    right(1) = right(1) + u_a;
    right(end) = right(end) + u_b;

    u = [u_a;(A\right);u_b];
    err = [err, max(abs(u-u_ref(1:2^(12-k):end)))];    
end

%plot(x,u_best,x,u,'r')
loglog(2.^(3:11),err)