function [ ] = prob_1_15_ode45
% 
% Written by:
% -- 
% John L. Weatherwax                2005-05-07
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

% Parameters:
global a c;
a=2; 
c=1;
% Initial conditions:
y0 = [ 1 3 ];
% Final time:
tmax = 10.0;

% A sample of step sizes:
hArray = 10.^[-1:-1:-4];
%hArray = 10.^[-1];

for hi=hArray,
  [ t, y ] = ode45(@prob_1_15_odefun,[0:hi:tmax],y0);
  figure; plot( y(:,1), y(:,2), '-o' ); title( [ 'hi = ', num2str(hi) ] );
  plotBigG( t, y(:,1), y(:,2), hi );
end

return;


%------------------------------------------------------------------------
%------------------------------------------------------------------------

function [ yprime ] = prob_1_15_odefun( t, y )

global a c;

yprime = [ a*y(1)*(1-y(2)); -c*y(2)*(1-y(1)) ];

return;


%------------------------------------------------------------------------
%------------------------------------------------------------------------

function [] = plotBigG( t, x, y, hi )

global a c;

G = x.^(-c) .* y.^(-a) .* exp( c*x + a*y );
figure; plot( t, G, '-o' );
xlabel( 'time (s)' ); ylabel( 'G (unitless)' );
title( [ 'hi = ', num2str(hi) ] );

return;