mrkiss_eerk_verner_7_6 Module Reference

Butcher tableau for Verner's 10 stage, Order (7,6) Runge-Kutta method. More...

Variables
integer, parameter	s = 10
	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, 6]
	The method orders.
integer, dimension(m), parameter	se = [9, 10]
	Number of stages for each method.

Detailed Description

Butcher tableau for Verner's 10 stage, Order (7,6) Runge-Kutta method.

IMO

This is my go-to O(7,6) method.

Known Aliases

'ARKODE_VERNER_10_6_7' (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
• Verner (2007, CORRECTED 2024); A "more efficient" Runge-Kutta (7)6 Pair with corrected Interpolants; https://www.sfu.ca/~jverner/; zotero://select/items/0_9NS8U6I6
  • Retreived 2025-07-26: https://www.sfu.ca/~jverner/RKV76.IIa.Efficient.00001675585.240711.FLOAT6040OnWeb
  • Retreived 2025-07-26: https://www.sfu.ca/~jverner/RKV76.IIa.Efficient.00001675585.240711.CoeffsOnlyRATandRAD
  • Retreived 2025-07-26: https://www.sfu.ca/~jverner/RKV76.IIa.Efficient.00001675585.240712.CoeffsOnlyFLOAT

Variable Documentation

s

integer, parameter mrkiss_eerk_verner_7_6::s = 10

The order of the overall method.

Definition at line 67 of file mrkiss_eerk_verner_7_6.f90.

m

integer, parameter mrkiss_eerk_verner_7_6::m = 2

Number of methods.

Definition at line 69 of file mrkiss_eerk_verner_7_6.f90.

a

real(kind=rk), dimension(s,s), parameter mrkiss_eerk_verner_7_6::a

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

Definition at line 71 of file mrkiss_eerk_verner_7_6.f90.

b

real(kind=rk), dimension(s,m), parameter mrkiss_eerk_verner_7_6::b

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

Definition at line 82 of file mrkiss_eerk_verner_7_6.f90.

c

real(kind=rk), dimension(s), parameter mrkiss_eerk_verner_7_6::c

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

Definition at line 85 of file mrkiss_eerk_verner_7_6.f90.

p

integer, dimension(m), parameter mrkiss_eerk_verner_7_6::p = [7, 6]

The method orders.

Definition at line 87 of file mrkiss_eerk_verner_7_6.f90.

se

integer, dimension(m), parameter mrkiss_eerk_verner_7_6::se = [9, 10]

Number of stages for each method.

Definition at line 89 of file mrkiss_eerk_verner_7_6.f90.