%
% 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');

% Problem 5.1: 
fh = figure;
subplot(1,2,1);

y0 = 50;
global k; k = 0.05;
y_truth = @(t) ( y0*exp(-k*t) );

[tvals, yvals] = fhermite( @(t,x) c_5_p_1_f_n_fp(t,x), [0,10], y0, 1 ); yvals(end)
plot( tvals, yvals, '-r' ); hold('on');
plot( tvals, y_truth(tvals), '-g' ); 
xlabel('t'); ylabel('y(t) for 5.1');

% Problem 5.2: 
subplot(1,2,2);

y0 = 2;
y_truth = @(t) ( 2*exp(t.^2) );

[tvals, yvals] = fhermite( @(t,x) c_5_p_2_f_n_fp(t,x), [0,2], y0, 0.2 ); yvals(end)
plot( tvals, yvals, '-.r' ); hold('on');

[tvals, yvals] = fhermite( @(t,x) c_5_p_2_f_n_fp(t,x), [0,2], y0, 0.02 ); yvals(end)
plot( tvals, yvals, '.k' );
plot( tvals, y_truth(tvals), '-g' ); 
xlabel('t'); ylabel('y(t) for 5.2'); axis tight;

%saveas( gcf, '../../WriteUp/Graphics/Chapter5/c_5_p_5_plot.eps', 'epsc' );