rk_module – fortran-astrodynamics-toolkit

Runge-Kutta integration.

Uses

- numbers_module
- kind_module
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Used by

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Graph Key

Nodes of different colours represent the following:

Solid arrows point from a submodule to the (sub)module which it is descended from. Dashed arrows point from a module or program unit to modules which it uses.

Interfaces

interface

private subroutine deriv_func(me, t, x, xdot)

derivative function

Arguments

Type	Intent	Attributes		Name
class(rk_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	state vector
real(kind=wp),	intent(out),	dimension(me%n)	::	xdot	derivative of state vector

interface

private subroutine event_func(me, t, x, g)

event function

Arguments

Type	Intent	Attributes		Name
class(rk_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	state vector
real(kind=wp),	intent(out)		::	g	g(t,x). The goal is to stop the integration when g=0.

interface

private subroutine report_func(me, t, x)

report function

Arguments

Type	Intent	Attributes		Name
class(rk_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	state vector

interface

private subroutine step_func(me, t, x, h, xf)

rk step function

Arguments

Type	Intent	Attributes		Name
class(rk_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state vector
real(kind=wp),	intent(in)		::	h	time step $\|\Delta t\|$
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	final state vector

Derived Types

type, public :: rk_class

main integration class:

Components

Type	Visibility	Attributes		Name		Initial
integer,	public		::	n	=	0	user specified number of variables
procedure(deriv_func),	public,	pointer	::	f	=>	null()	user-specified derivative function
procedure(report_func),	public,	pointer	::	report	=>	null()	user-specified report function
procedure(event_func),	public,	pointer	::	g	=>	null()	event function (stop when this is zero)

Type-Bound Procedures

procedure, public :: initialize	../../ initialize the class (set n,f, and report)
procedure, public, non_overridable :: integrate	../../ main integration routine
procedure, public, non_overridable :: integrate_to_event	../../ integration with event finding
procedure(step_func), public, deferred :: step	../../ the step routine for the rk method
procedure, public :: destroy	../../ destructor

type, public, extends(rk_class) :: rk4_class

4th order Runge-Kutta method.

Components

Type	Visibility	Attributes		Name		Initial
integer,	public		::	n	=	0	user specified number of variables
procedure(deriv_func),	public,	pointer	::	f	=>	null()	user-specified derivative function
procedure(report_func),	public,	pointer	::	report	=>	null()	user-specified report function
procedure(event_func),	public,	pointer	::	g	=>	null()	event function (stop when this is zero)

Type-Bound Procedures

procedure, public :: initialize	../../ initialize the class (set n,f, and report)
procedure, public, non_overridable :: integrate	../../ main integration routine
procedure, public, non_overridable :: integrate_to_event	../../ integration with event finding
procedure, public :: destroy	../../ destructor
procedure, public :: step => rk4

type, public, extends(rk_class) :: rk8_10_class

8th order Runge-Kutta method.

Components

Type	Visibility	Attributes		Name		Initial
integer,	public		::	n	=	0	user specified number of variables
procedure(deriv_func),	public,	pointer	::	f	=>	null()	user-specified derivative function
procedure(report_func),	public,	pointer	::	report	=>	null()	user-specified report function
procedure(event_func),	public,	pointer	::	g	=>	null()	event function (stop when this is zero)

Type-Bound Procedures

procedure, public :: initialize	../../ initialize the class (set n,f, and report)
procedure, public, non_overridable :: integrate	../../ main integration routine
procedure, public, non_overridable :: integrate_to_event	../../ integration with event finding
procedure, public :: destroy	../../ destructor
procedure, public :: step => rk8_10

Subroutines

private subroutine initialize(me, n, f, report, g)

Initialize the rk_class.

Arguments

Type	Intent	Optional		Name
class(rk_class),	intent(inout)		::	me
integer,	intent(in)		::	n	number of variables
procedure(deriv_func)			::	f	derivative function
procedure(report_func),		optional	::	report	for reporting the steps
procedure(event_func),		optional	::	g	for stopping at an event

private subroutine destroy(me)

Destructor for rk_class.

Arguments

Type	Intent	Optional	Attributes		Name
class(rk_class),	intent(out)			::	me

private subroutine integrate(me, t0, x0, h, tf, xf)

Main integration routine for the rk_class.

Arguments

Type	Intent	Attributes		Name
class(rk_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t0	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x0	initial state
real(kind=wp),	intent(in)		::	h	abs(time step)
real(kind=wp),	intent(in)		::	tf	final time
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	final state

private subroutine integrate_to_event(me, t0, x0, h, tmax, tol, tf, xf, gf)

Event-finding integration routine for the rk_class. Integrates until g(t,x)=0, or until t=tf (whichever happens first).

Arguments

Type	Intent	Attributes		Name
class(rk_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t0	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x0	initial state
real(kind=wp),	intent(in)		::	h	abs(time step)
real(kind=wp),	intent(in)		::	tmax	max final time if event not located
real(kind=wp),	intent(in)		::	tol	function tolerance for root finding
real(kind=wp),	intent(out)		::	tf	actual final time reached
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	final state (at tf)
real(kind=wp),	intent(out)		::	gf	g value at tf

private subroutine rk4(me, t, x, h, xf)

Take one Runge Kutta 4 integration step: t -> t+h (x -> xf)

Arguments

Type	Intent	Attributes		Name
class(rk4_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`

private subroutine rk8_10(me, t, x, h, xf)

Take one Runge Kutta 8 integration step: t -> t+h (x -> xf) This is Formula (8-10) from Reference [1].

Arguments

Type	Intent	Attributes		Name
class(rk8_10_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`

public subroutine rk_test()

Unit test of the rk_module. Integrate a two-body orbit around the Earth.

Arguments

None

rk_module Module

Contents

Interfaces

Derived Types

Subroutines

Uses

Used by

Interfaces

interface

private subroutine deriv_func(me, t, x, xdot)

Arguments

interface

private subroutine event_func(me, t, x, g)

Arguments

interface

private subroutine report_func(me, t, x)

Arguments

interface

private subroutine step_func(me, t, x, h, xf)

Arguments

Derived Types

type, public :: rk_class

Components

Type-Bound Procedures

type, public, extends(rk_class) :: rk4_class

Components

Type-Bound Procedures

type, public, extends(rk_class) :: rk8_10_class

Components

Type-Bound Procedures

Subroutines

private subroutine initialize(me, n, f, report, g)

Arguments

private subroutine destroy(me)

Arguments

private subroutine integrate(me, t0, x0, h, tf, xf)

Arguments

private subroutine integrate_to_event(me, t0, x0, h, tmax, tol, tf, xf, gf)

Arguments

private subroutine rk4(me, t, x, h, xf)

Arguments

private subroutine rk8_10(me, t, x, h, xf)

Arguments

public subroutine rk_test()

Arguments