%
% 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.
%
%-----

close all; clc; clear all; 

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

fprime = @(t,y) ( 2*t*y );
y0 = 2; 

y_truth = @(t) ( 2*exp(t.^2) );

[tvals, yvals] = rkgen( fprime, [0,2], y0, 0.2, 1 ); v_1 = yvals(end); 
relative_error = ( yvals - y_truth(tvals) ) ./ y_truth(tvals);
ph_rk_classical = plot( tvals, relative_error, '-r' ); hold('on');

[tvals, yvals] = rkgen( fprime, [0,2], y0, 0.2, 2 ); v_2 = yvals(end); 
relative_error = ( yvals - y_truth(tvals) ) ./ y_truth(tvals);
ph_rk_butcher = plot( tvals, relative_error, '-g' ); 

[tvals, yvals] = rkgen( fprime, [0,2], y0, 0.2, 3 ); v_3 = yvals(end); 
relative_error = ( yvals - y_truth(tvals) ) ./ y_truth(tvals);
ph_rk_merson = plot( tvals, relative_error, '-b' ); 

[ v_1, v_2, v_3, y_truth(2) ] 

legend( [ph_rk_classical,ph_rk_butcher,ph_rk_merson], 'RK classic', 'RK Butcher', 'RK merson', 'location', 'southwest' );
xlabel('time'); ylabel('y(t)'); title('relative error of various RK methods')
grid('on'); 

%saveas( gcf, '../../WriteUp/Graphics/Chapter5/c_5_p_2_plot.eps', 'epsc' );