%
% 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; Shooting method on EPage 106; 
% 
s = -3.0:0.5:2.0; % evalute the value of y(1) at each of these slopes at zero i.e. y'(0) (we want y(1) ~ 2)
ncases = length(s); b = zeros(1,ncases);
for i=1:ncases,
  [x,y] = ode45( 'c_6_p_2_ode_fn', [0, 1], [1, s(i)] );
  [m,n] = size(y);
  b(1,i) = y(m,1); % save the value of y(1) for this slope 
end
s0 = aitken(b,s,2); % use aitken's method to find the slope that gives y(1) == 2
[x,y] = ode45( 'c_6_p_2_ode_fn', [0, 1], [1, s0] );
plot( x, y(:,1), '-k' );
hold('on'); grid('on');

% Use the function "twopoint.m": 
% 
n = 10;
x = linspace( 0, 1, n+1 );
C = ones( 1, n+1 );
D = ones( 1, n+1 ); 
E = -6 * ones( 1, n+1 ); 
F = zeros( 1, n+1 ); 
y_tp = twopoint( x, C, D, E, F, 1, 1, 1, 2 );
plot( x, y_tp, '-b' ); 

xs = linspace( 0, 1, 100 );
ys = 0.2657 * exp( 2*xs ) + 0.7343 * exp( -3*xs );
plot( xs, ys, '-g' );

legend( 'shooting method', 'twopoint', 'truth', 'location', 'best' ); 

%saveas( gcf, '../../WriteUp/Graphics/Chapter6/c_6_p_2_plot.eps', 'epsc' );