StepSize Module. More...

Functions/Subroutines
subroutine	stepsz0hairer (h, p, n, x0, y0, f0, sc, hsign, hmax, fcalls, pdiffeqsys, params)
	Subroutine for computing the starting step size using Hairer's algorithm.

real(wp) function	stepszhairer (h, islaststeprejected, q, e, stepszparams)
	Pure function for computing the new step size using Hairer's algorithm.

Variables
real(wp), parameter	sf = 0.9_WP
	Safety factor.

real(wp), parameter	sfmin = 0.333_WP
	Minimum safety factor, so we dont decrease the step size too fast.

real(wp), parameter	sfmax = 6.0_WP
	Maximum safety factor, so we dont increase the step size too fast

real(wp), parameter	hbyhoptold = 1.0e-4_WP
	Lund stabilization PI control term (see Hairer's code)

Detailed Description

StepSize Module.

This module provides procedures for step size computation.

Date: Created: 01/28/2019
Module containing all the algorithms for step size computations

Function/Subroutine Documentation

subroutine stepsize::stepsz0hairer	(	real(wp), intent(out)	h,
		integer, intent(in)	p,
		integer, intent(in)	n,
		real(wp), intent(in)	x0,
		real(wp), dimension(n), intent(in)	y0,
		real(wp), dimension(n), intent(in)	f0,
		real(wp), dimension(n), intent(in)	sc,
		real(wp), intent(in)	hsign,
		real(wp), intent(in)	hmax,
		integer, intent(out)	fcalls,
		class(diffeqsys), intent(inout), pointer	pdiffeqsys,
		real(wp), dimension(:), intent(in), optional	params )

Subroutine for computing the starting step size using Hairer's algorithm.

For details on the algorithm, see Hairer's book "Solving ODE I" or his code dop853.f at http://www.unige.ch/~hairer/prog/nonstiff/dop853.f.

Parameters

[out]	h	Computed step size
[in]	p	Order of the method, which is used to advance the integration. For example, for Dormand-Prince 8(7) ERK method, p=8.
[in]	n	dimension of the DiffEq system
[in]	x0	Initial value of the independent variable
[in]	y0	Initial condition
[in]	f0	DiffEq Function evaluated at Y0
[in]	sc	Error Scale factor
[in]	hsign	Must be either +1.0 or -1.0 depending on the forward or backward integration, respectively
[in]	hmax	Maximum allowed step size
[out]	fcalls	Number of Calls that this routine makes to DiffEq function "F"
[in,out]	pdiffeqsys	DiffEq system
[in]	params	Real parameter array to be passed to DEFunc

Remarks: The equation to solve for the new guess for the starting step size is
$h_1^{p+1} max(d1, d2) = 0.01$
In Hairer's dop853 code, he actually uses instead of as the power of for reasons unknown. He uses for his dop853.

Definition at line 53 of file StepSz.f90.

real(wp) function stepsize::stepszhairer	(	real(wp), intent(in)	h,
		logical, intent(in)	islaststeprejected,
		integer, intent(in)	q,
		real(wp), intent(in)	e,
		real(wp), dimension(6), intent(inout)	stepszparams )

Pure function for computing the new step size using Hairer's algorithm.

For details on the algorithm, see Hairer's book "Solving ODE I" or his code dop853.f at http://www.unige.ch/~hairer/prog/nonstiff/dop853.f.

Parameters

[in]	h	current step size
[in]	islaststeprejected	If true then the step size is decreased else increased.
[in]	q	q = min(p,phat) but Hairer uses q=8 in DOP853.
[in]	e	Error norm
[in,out]	stepszparams	Contains safety factor and Lund stabilization related parameters