% A5PROB4C  Script to use A5PROB4 to solve problem 4c on A#5

tf = 1.0;
manu0 = @(x) 0;  manu = @(x,t) t * cos(pi*x/2);
J = [5 10 20 40 80 160 320 640 1280];  % expanded refinement path
err = zeros(size(J));
for m = 1:length(J)
  U = a5prob4(J(m),tf,@manf,manu0);
  x = linspace(0,1,J(m)+1);
  err(m) = max(abs(U - manu(x,tf)));
end

dx=1./J;  
c=polyfit(log(dx),log(err),1)  % fit line to data
disp(['convergence at rate O(dx^{' num2str(c(1),7) '})'])

loglog(dx,err,'o',dx,exp(c(1)*log(dx)+c(2)),'--')
xlabel('\Delta x'), ylabel('error = max |U_j^N - u(x_j,t_f)|')
axis tight, set(gca,'XTick',[1e-3 5e-3 1e-2 5e-2 1e-1])