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               $gsl_odeiv_step_rk8pd
               $gsl_odeiv_step_rk2imp
               $gsl_odeiv_step_rk2simp
               $gsl_odeiv_step_rk4imp
               $gsl_odeiv_step_bsimp
               $gsl_odeiv_step_gear1
               $gsl_odeiv_step_gear2
               $GSL_ODEIV_HADJ_INC
               $GSL_ODEIV_HADJ_NIL
               $GSL_ODEIV_HADJ_DEC
               $gsl_odeiv_control_standard
	/;
%EXPORT_TAGS = ( all => [ @EXPORT_OK ] );

__END__

=encoding utf8

=head1 NAME

Math::GSL::ODEIV - functions for solving ordinary differential equation (ODE) initial value problems

=head1 SYNOPSIS

 use Math::GSL::ODEIV qw /:all/;

=head1 DESCRIPTION

Here is a list of all the functions in this module :

=over

=item * C<gsl_odeiv_step_alloc($T, $dim)> - This function returns a pointer to a newly allocated instance of a stepping function of type $T for a system of $dim dimensions.$T must be one of the step type constant above.

=item * C<gsl_odeiv_step_reset($s)> - This function resets the stepping function $s. It should be used whenever the next use of s will not be a continuation of a previous step.

=item * C<gsl_odeiv_step_free($s)> - This function frees all the memory associated with the stepping function $s.

=item * C<gsl_odeiv_step_name($s)> - This function returns a pointer to the name of the stepping function.

=item * C<gsl_odeiv_step_order($s)> - This function returns the order of the stepping function on the previous step. This order can vary if the stepping function itself is adaptive.

=item * C<gsl_odeiv_step_apply >

=item * C<gsl_odeiv_control_alloc($T)> - This function returns a pointer to a newly allocated instance of a control function of type $T. This function is only needed for defining new types of control functions. For most purposes the standard control ...

=item * C<gsl_odeiv_control_init($c, $eps_abs, $eps_rel, $a_y, $a_dydt) > - This function initializes the control function c with the parameters eps_abs (absolute error), eps_rel (relative error), a_y (scaling factor for y) and a_dydt (scaling factor...

=item * C<gsl_odeiv_control_free >

=item * C<gsl_odeiv_control_hadjust >

=item * C<gsl_odeiv_control_name >

=item * C<gsl_odeiv_control_standard_new($eps_abs, $eps_rel, $a_y, $a_dydt)> - The standard control object is a four parameter heuristic based on absolute and relative errors $eps_abs and $eps_rel, and scaling factors $a_y and $a_dydt for the system ...

=item * C<gsl_odeiv_control_y_new($eps_abs, $eps_rel)> - This function creates a new control object which will keep the local error on each step within an absolute error of $eps_abs and relative error of $eps_rel with respect to the solution y_i(t). ...

=item * C<gsl_odeiv_control_yp_new($eps_abs, $eps_rel)> - This function creates a new control object which will keep the local error on each step within an absolute error of $eps_abs and relative error of $eps_rel with respect to the derivatives of t...

=item * C<gsl_odeiv_control_scaled_new($eps_abs, $eps_rel, $a_y, $a_dydt, $scale_abs, $dim) > - This function creates a new control object which uses the same algorithm as gsl_odeiv_control_standard_new but with an absolute error which is scaled for ...

=item * C<gsl_odeiv_evolve_alloc($dim)> - This function returns a pointer to a newly allocated instance of an evolution function for a system of $dim dimensions.

=item * C<gsl_odeiv_evolve_apply($e, $c, $step, $dydt, \$t, $t1, \$h, $y)> - This function advances the system ($e, $dydt) from time $t and position $y using the stepping function $step. The new time and position are stored in $t and $y on output. Th...

=item * C<gsl_odeiv_evolve_reset($e)> - This function resets the evolution function $e. It should be used whenever the next use of $e will not be a continuation of a previous step.

=item * C<gsl_odeiv_evolve_free($e)> - This function frees all the memory associated with the evolution function $e.

=back

This module also includes the following constants :

=over

=item * C<$GSL_ODEIV_HADJ_INC>

=item * C<$GSL_ODEIV_HADJ_NIL>

=item * C<$GSL_ODEIV_HADJ_DEC>

=back

=head2 Step Type

=over

=item * C<$gsl_odeiv_step_rk2> - Embedded Runge-Kutta (2, 3) method.

=item * C<$gsl_odeiv_step_rk4> - 4th order (classical) Runge-Kutta. The error estimate is obtained by halving the step-size. For more efficient estimate of the error, use the Runge-Kutta-Fehlberg method described below.

=item * C<$gsl_odeiv_step_rkf45> - Embedded Runge-Kutta-Fehlberg (4, 5) method. This method is a good general-purpose integrator.

=item * C<$gsl_odeiv_step_rkck> - Embedded Runge-Kutta Cash-Karp (4, 5) method.

=item * C<$gsl_odeiv_step_rk8pd> - Embedded Runge-Kutta Prince-Dormand (8,9) method.

=item * C<$gsl_odeiv_step_rk2imp> - Implicit 2nd order Runge-Kutta at Gaussian points.

=item * C<$gsl_odeiv_step_rk2simp>

=item * C<$gsl_odeiv_step_rk4imp> - Implicit 4th order Runge-Kutta at Gaussian points.

=item * C<$gsl_odeiv_step_bsimp> - Implicit Bulirsch-Stoer method of Bader and Deuflhard. This algorithm requires the Jacobian.

=item * C<$gsl_odeiv_step_gear1> - M=1 implicit Gear method.

=item * C<$gsl_odeiv_step_gear2> - M=2 implicit Gear method.

=back

For more informations on the functions, we refer you to the GSL official
documentation: L<http://www.gnu.org/software/gsl/manual/html_node/>

=head1 EXAMPLE

The example is taken from L<https://www.math.utah.edu/software/gsl/gsl-ref_367.html>.

 use strict;
 use warnings;