mrkiss_eerk_verner_8_7 Module Reference

Butcher tableau for Verner's 13 stage, Order (8,7) 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 = [8, 7]
	The method orders.
integer, dimension(m), parameter	se = [12, 13]
	Number of stages for each method.

Detailed Description

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

IMO

This is my go-to O(8,7) method.

Known Aliases

'ARKODE_VERNER_13_7_8' (SUNDIALS).

Stability Image Links

References:

• Verner (2010); Numerically Optimal Runge-Kutta Pairs with Interpolants; Num. Alg. 53 (2-3); p383-396;
• Verner (2007); A "more efficient" Runge–Kutta (8)7 Pair with Interpolants; https://www.sfu.ca/~jverner/; zotero://select/items/0_8SNJI34E
  • Retreived 2025-07-26: https://www.sfu.ca/~jverner/RKV87.IIa.Efficient.000000282866.081208.CoeffsOnlyRATandFLOAT
  • Retreived 2025-07-26: https://www.sfu.ca/~jverner/RKV87.IIa.Efficient.000000282866.081208.CoeffsOnlyFLOAT

Variable Documentation

s

integer, parameter mrkiss_eerk_verner_8_7::s = 13

The order of the overall method.

Definition at line 65 of file mrkiss_eerk_verner_8_7.f90.

m

integer, parameter mrkiss_eerk_verner_8_7::m = 2

Number of methods.

Definition at line 67 of file mrkiss_eerk_verner_8_7.f90.

a

real(kind=rk), dimension(s,s), parameter mrkiss_eerk_verner_8_7::a

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

Definition at line 69 of file mrkiss_eerk_verner_8_7.f90.

b

real(kind=rk), dimension(s,m), parameter mrkiss_eerk_verner_8_7::b

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

Definition at line 83 of file mrkiss_eerk_verner_8_7.f90.

c

real(kind=rk), dimension(s), parameter mrkiss_eerk_verner_8_7::c

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

Definition at line 86 of file mrkiss_eerk_verner_8_7.f90.

p

integer, dimension(m), parameter mrkiss_eerk_verner_8_7::p = [8, 7]

The method orders.

Definition at line 90 of file mrkiss_eerk_verner_8_7.f90.

se

integer, dimension(m), parameter mrkiss_eerk_verner_8_7::se = [12, 13]

Number of stages for each method.

Definition at line 92 of file mrkiss_eerk_verner_8_7.f90.