added test_periodic.m which is an convergence order test using periodic BCs

test_periodic.m

@@ -0,0 +1,61 @@
+function [pass] = test_periodic(plots,verbose)
+% This test solves the problem for a solution u(x) = sin(2x) in [0,pi], with 
+% periodic BCs u(0) = u(pi). The PDE is u''+u = -3sin(2*x). A Poisson
+% problem u'' = f might be problematic because with periodic BCs for any
+% solution u, u + c is also a solution.
+%
+if nargin == 0
+    plots = false;
+    verbose = false;
+elseif nargin == 1
+    verbose = false;
+end
+
+N = 100;
+h = pi/N;
+[Ix,D1xx,D1xc,D1xb,D1xf] = diff_matrices1d(N, pi/N);
+
+x = 0:h:pi-h; % grid point at x = 0 to x = pi-h;
+f = -3*sin(2*x);
+u_num = (D1xx+eye(N,N))\f';
+u_e = sin(2*x)';
+
+if plots
+    subplot(1,2,1)
+    plot(x,u_e,'r')
+    hold on
+    plot(x,u_num)
+    xlim([0 pi]);
+    hold off
+    title('Coarse Numerical vs analytical solutions')
+
+    subplot(1,2,2)
+    plot(x,abs(u_e-u_num))
+    xlim([0 pi]);
+    title('Absolute error')
+end
+err_coarse = max(abs(u_e-u_num));
+
+%fine grid;
+r = 2; % 2 times refinement
+N = r*N;
+h = pi/N;
+[Ix,D1xx,D1xc,D1xb,D1xf] = diff_matrices1d(N, pi/N);
+x = 0:h:pi-h; % grid point at x = 0 to x = pi-h;
+f = -3*sin(2*x);
+u_num = (D1xx+eye(N,N))\f';
+u_e = sin(2*x)';
+err_fine = max(abs(u_e-u_num));
+
+if abs(log(err_coarse/err_fine)/log(2) - 2) > 0.1 % arbitrary margin for order of convergence
+    pass = false;
+    if verbose
+        sprintf('Test not passed: the error was reduced by factor %.4g for a %.1g finer grid',err_coarse/err_fine,r)
+    end
+else
+    pass = true;
+    if verbose
+        sprintf('Test passed succesfully: the error was reduced by factor %.4g for a %.1g finer grid',err_coarse/err_fine,r)
+    end
+end
+end