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)