mrkiss_eerk_tsitouras_arkode_5_4 Module Reference

Butcher tableau for ARKODE's Tsitouras 7 stage Order (5,4) Runge-Kutta method. More...

Variables
integer, parameter	s = 7
	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 \(\mathbf{b_1}\) 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 = [5, 4]
	The method orders.
integer, dimension(m), parameter	se = [6, 7]
	Number of stages for each method.

Detailed Description

Butcher tableau for ARKODE's Tsitouras 7 stage Order (5,4) Runge-Kutta method.

IMO

This tableau came directly from the ARKODE source. It's not the same one from tsitouras' paper. It is also not the same one used in OrdinaryDiffEq.jl. So far my testing has shown to be a solid method.

Known Aliases

'ARKODE_TSITOURAS_7_4_5' (SUNDIALS)

Stability Image Links

References:

• Tsitouras (2011); Runge-Kutta Pairs of Order 5(4) Satisfying Only the First Column Simplifying Assumption; Comp. & Math. w/ Appl. 62 (2); p770-775; zotero://select/items/0_WHVVHHDH

Variable Documentation

s

integer, parameter mrkiss_eerk_tsitouras_arkode_5_4::s = 7

The order of the overall method.

Definition at line 63 of file mrkiss_eerk_tsitouras_arkode_5_4.f90.

m

integer, parameter mrkiss_eerk_tsitouras_arkode_5_4::m = 2

Number of methods.

Definition at line 65 of file mrkiss_eerk_tsitouras_arkode_5_4.f90.

a

real(kind=rk), dimension(s,s), parameter mrkiss_eerk_tsitouras_arkode_5_4::a

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

Definition at line 67 of file mrkiss_eerk_tsitouras_arkode_5_4.f90.

b

real(kind=rk), dimension(s,m), parameter mrkiss_eerk_tsitouras_arkode_5_4::b

The \(\mathbf{b_1}\) matrix for the Butcher Tableau.

Definition at line 75 of file mrkiss_eerk_tsitouras_arkode_5_4.f90.

c

real(kind=rk), dimension(s), parameter mrkiss_eerk_tsitouras_arkode_5_4::c

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

Definition at line 78 of file mrkiss_eerk_tsitouras_arkode_5_4.f90.

p

integer, dimension(m), parameter mrkiss_eerk_tsitouras_arkode_5_4::p = [5, 4]

The method orders.

Definition at line 80 of file mrkiss_eerk_tsitouras_arkode_5_4.f90.

se

integer, dimension(m), parameter mrkiss_eerk_tsitouras_arkode_5_4::se = [6, 7]

Number of stages for each method.

Definition at line 82 of file mrkiss_eerk_tsitouras_arkode_5_4.f90.