mrkiss_eerk_dormand_prince_7_8 Module Reference

Butcher tableau for Dormand & Prince's 13 stage, Order (7,8) Runge-Kutta method. More...

Variables
integer, parameter	s = 13
	The order of the overall method.
integer, parameter	m = 2
	Number of methods.
real(kind=rk), dimension(s, s), parameter	a
	The \(\mathbf{a}\) matrix for the Butcher Tableau.
real(kind=rk), dimension(s, m), parameter	b
	The \(\mathbf{b}\) matrix for the Butcher Tableau.
real(kind=rk), dimension(s), parameter	c
	The \(\mathbf{c}\) matrix for the Butcher Tableau.
integer, dimension(m), parameter	p = [7, 8]
	The method orders.
integer, dimension(m), parameter	se = [13, 12]
	Number of stages for each method.

Detailed Description

Butcher tableau for Dormand & Prince's 13 stage, Order (7,8) Runge-Kutta method.

Stability Image Links

References:

• Prince & Dormand(1981); High Order Embedded Runge-Kutta Formulae; J. of Comp. and Appl. Math. 7 (1); p67-75; zotero://select/items/0_N9KVWVST
• Peter Stone (2011); "The 'Classical' Prince-Dormand 13 Stage Combined Order 7 and 8 Runge-Kutta Scheme"; http://www.peterstone.name/Maplepgs/RKcoeff.html; zotero://select/items/0_LTA7NCAS

Variable Documentation

s

integer, parameter mrkiss_eerk_dormand_prince_7_8::s = 13

The order of the overall method.

Definition at line 58 of file mrkiss_eerk_dormand_prince_7_8.f90.

m

integer, parameter mrkiss_eerk_dormand_prince_7_8::m = 2

Number of methods.

Definition at line 60 of file mrkiss_eerk_dormand_prince_7_8.f90.

a

real(kind=rk), dimension(s,s), parameter mrkiss_eerk_dormand_prince_7_8::a

The \(\mathbf{a}\) matrix for the Butcher Tableau.

Definition at line 62 of file mrkiss_eerk_dormand_prince_7_8.f90.

b

real(kind=rk), dimension(s,m), parameter mrkiss_eerk_dormand_prince_7_8::b

The \(\mathbf{b}\) matrix for the Butcher Tableau.

Definition at line 76 of file mrkiss_eerk_dormand_prince_7_8.f90.

c

real(kind=rk), dimension(s), parameter mrkiss_eerk_dormand_prince_7_8::c

The \(\mathbf{c}\) matrix for the Butcher Tableau.

Definition at line 79 of file mrkiss_eerk_dormand_prince_7_8.f90.

p

integer, dimension(m), parameter mrkiss_eerk_dormand_prince_7_8::p = [7, 8]

The method orders.

Definition at line 81 of file mrkiss_eerk_dormand_prince_7_8.f90.

se

integer, dimension(m), parameter mrkiss_eerk_dormand_prince_7_8::se = [13, 12]

Number of stages for each method.

Definition at line 83 of file mrkiss_eerk_dormand_prince_7_8.f90.