mrkiss_eerk_verner_2010_6_5 Module Reference

Butcher tableau for Verner's 9 stage, Order (6,5) Runge-Kutta method (2010) More...

Variables
integer, parameter	s = 9
	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 = [6, 5]
	The method orders.
integer, dimension(m), parameter	se = [8, 9]
	Number of stages for each method.

Detailed Description

Butcher tableau for Verner's 9 stage, Order (6,5) Runge-Kutta method (2010)

IMO

This is a good general use method. Be sure and use 64-bit floats or larger. This is my go-to O(6,5) method.

Known Aliases

'ARKODE_VERNER_9_5_6' (SUNDIALS).

Stability Image Links

References:

• Verner (2010); Numerically Optimal Runge-Kutta Pairs with Interpolants; Num. Alg. 53 (2-3); p383-396; zotero://select/items/0_24ANPMLC

Variable Documentation

s

integer, parameter mrkiss_eerk_verner_2010_6_5::s = 9

The order of the overall method.

Definition at line 62 of file mrkiss_eerk_verner_2010_6_5.f90.

m

integer, parameter mrkiss_eerk_verner_2010_6_5::m = 2

Number of methods.

Definition at line 64 of file mrkiss_eerk_verner_2010_6_5.f90.

a

real(kind=rk), dimension(s,s), parameter mrkiss_eerk_verner_2010_6_5::a

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

Definition at line 66 of file mrkiss_eerk_verner_2010_6_5.f90.

b

real(kind=rk), dimension(s,m), parameter mrkiss_eerk_verner_2010_6_5::b

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

Definition at line 76 of file mrkiss_eerk_verner_2010_6_5.f90.

c

real(kind=rk), dimension(s), parameter mrkiss_eerk_verner_2010_6_5::c

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

Definition at line 79 of file mrkiss_eerk_verner_2010_6_5.f90.

p

integer, dimension(m), parameter mrkiss_eerk_verner_2010_6_5::p = [6, 5]

The method orders.

Definition at line 81 of file mrkiss_eerk_verner_2010_6_5.f90.

se

integer, dimension(m), parameter mrkiss_eerk_verner_2010_6_5::se = [8, 9]

Number of stages for each method.

Definition at line 83 of file mrkiss_eerk_verner_2010_6_5.f90.