%
% Written by:
% --
% John L. Weatherwax                2009-04-21
%
% email: wax@alum.mit.edu
%
% Please send comments and especially bug reports to the
% above email address.
%
%-----

addpath('../../BookCode');

close all; clc; clear; 

% Problem EPage 118 ; Equation 6.6.1 on EPage 112?
% 
c = 1;
nx = 20; % 20 division of x
hx = 1/nx;
ht = 0.05; % t = 0:0.05:4.5
nt = 90; 
t = linspace( 0, 4.5, nt+1 );
x = 0:hx:1;
init = sin( pi * x ) + 2 * sin( 2 * pi * x ); % u(x,0) = sin( pi * x ) + 2 sin( 2 pi x )
initslope = zeros( 1, nx+1 ); % u_t(0,x) = 0
lowb = 0; 
hib = 0; % u(t,0) = u(t,1) = 0;

[X,T] = meshgrid( x, t ); 
u_truth = sin( pi * X ) .* cos( pi * T ) + 2 * sin( 2 * pi * X ) .* cos( 2 * pi * T );

u = fwave(nx,hx,nt,ht,init,initslope,lowb,hib,c);
surf(u);
xlabel('x - node number'); ylabel('time - node number'); zlabel('displacement u(x,t)'); title('approximation');

%saveas( gcf, '../../WriteUp/Graphics/Chapter6/c_6_p_7_plot.eps', 'epsc' );

figure; 
surf(u_truth);
xlabel('x - node number'); ylabel('time - node number'); zlabel('displacement u(x,t)'); title('truth');

A = abs( u-u_truth );
max( A(:) )