#!/usr/bin/perl -w
# Example 1:  Solve
#   f'' - g' = 0
#   g'' + f*g' - f'*g = 0
#   f(0)=0,f'(0)=1,f''(0)=-1,g(0)=1
#   Solution: f = 1 - exp(-x)
#   g = exp(-x)
use Math::ODE;
my $o = new Math::ODE ( file => 'data',
                        step => 0.1,
                        initial => [0,1,-1,1],
                        ODE => [ \&DE1, \&DE2 , \&DE3, \&DE4 ],
                        t0 => 0,
                        tf => 20 );
$o->evolve;
system("gnuplot -persist gnuplot.3");
sub DE1 { my ($t,$y) = @_; $y->[1]; }
sub DE2 { my ($t,$y) = @_; $y->[2]; }
sub DE3 { my ($t,$y) = @_; $y->[1] * $y->[3] - $y->[0] * $y->[2]; }
sub DE4 { my ($t,$y) = @_; $y->[2]; }