mrkiss_eerk_bogacki_shampine_4_5 Module Reference

Butcher tableau for Bogacki Shampine's 7 step, order (4,5) 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 \(\mathbf{b}\) 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 = [4, 5]
	The method orders.
integer, dimension(m), parameter	se = [7, 7]
	Number of stages for each method.

Detailed Description

Butcher tableau for Bogacki Shampine's 7 step, order (4,5) Runge-Kutta method.

IMO

This is a good general use method with excellent error coefficients.

Known Aliases

'bs5' (OrdinaryDiffEq.jl)

Stability Image Links

References:

• Bogacki & Shampine (1996); An Efficient Runge-Kutta (4,5) Pair; Comp. & Math. with Appl. 32 (6); p15-28; zotero://select/items/0_3SDMHUHW
• Peter Stone (2012); Bogacki-Shampine Combined 7 Stage, Order 4 and 5 Runge-Kutta Scheme with an Additional 8 Stage, Order 4 FSAL Embedded Scheme; zotero://select/items/0_AS3ZHL53

Variable Documentation

s

integer, parameter mrkiss_eerk_bogacki_shampine_4_5::s = 7

The order of the overall method.

Definition at line 64 of file mrkiss_eerk_bogacki_shampine_4_5.f90.

m

integer, parameter mrkiss_eerk_bogacki_shampine_4_5::m = 2

Number of methods.

Definition at line 66 of file mrkiss_eerk_bogacki_shampine_4_5.f90.

a

real(kind=rk), dimension(s,s), parameter mrkiss_eerk_bogacki_shampine_4_5::a

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

Definition at line 68 of file mrkiss_eerk_bogacki_shampine_4_5.f90.

b

real(kind=rk), dimension(s,m), parameter mrkiss_eerk_bogacki_shampine_4_5::b

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

Definition at line 76 of file mrkiss_eerk_bogacki_shampine_4_5.f90.

c

real(kind=rk), dimension(s), parameter mrkiss_eerk_bogacki_shampine_4_5::c

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

Definition at line 79 of file mrkiss_eerk_bogacki_shampine_4_5.f90.

p

integer, dimension(m), parameter mrkiss_eerk_bogacki_shampine_4_5::p = [4, 5]

The method orders.

Definition at line 81 of file mrkiss_eerk_bogacki_shampine_4_5.f90.

se

integer, dimension(m), parameter mrkiss_eerk_bogacki_shampine_4_5::se = [7, 7]

Number of stages for each method.

Definition at line 83 of file mrkiss_eerk_bogacki_shampine_4_5.f90.