mrkiss_erk_kutta_4 Module Reference

Butcher tableau for the classic 4 stage Runge-Kutta method of O(4) More...

Variables
integer, parameter	s = 4
	The order of the overall method.
integer, parameter	m = 1
	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]
	The method orders.
integer, dimension(m), parameter	se = [4]
	Number of stages for each method.

Detailed Description

Butcher tableau for the classic 4 stage Runge-Kutta method of O(4)

IMO

Useful for low accuracy applications; however, I find I rarely use it.

Known Aliases

'RK4' (OrdinaryDiffEq.jl), 'RK41' (Butcher), & 'The Runge-Kutta Method'.

Stability Image Links

References:

• Kutta (1901); Beitrag Zur N"herungsweisen Integration Totaler Differentialgleichungen; Z. Math. Phys. 46; p435-53
• Hairer, Norsett & Wanner (2009). Solving Ordinary Differential Equations. I: Nonstiff Problems. p138; zotero://select/items/0_VLZWN2CT
• Butcher (2016); Numerical Methods for Ordinary Differential Equations. 3ed; p102; zotero://select/items/0_V7UTIRPT

Variable Documentation

s

integer, parameter mrkiss_erk_kutta_4::s = 4

The order of the overall method.

Definition at line 64 of file mrkiss_erk_kutta_4.f90.

m

integer, parameter mrkiss_erk_kutta_4::m = 1

Number of methods.

Definition at line 66 of file mrkiss_erk_kutta_4.f90.

a

real(kind=rk), dimension(s,s), parameter mrkiss_erk_kutta_4::a

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

Definition at line 68 of file mrkiss_erk_kutta_4.f90.

  real(kind=rk),    parameter :: a(s,s) = reshape([ 0.0_rk, 0.0_rk, 0.0_rk, 0.0_rk,  &
       &                                            1.0_rk, 0.0_rk, 0.0_rk, 0.0_rk,  &
       &                                            0.0_rk, 1.0_rk, 0.0_rk, 0.0_rk,  &
       &                                            0.0_rk, 0.0_rk, 2.0_rk, 0.0_rk], [s, s]) / 2.0_rk

b

real(kind=rk), dimension(s,m), parameter mrkiss_erk_kutta_4::b

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

Definition at line 73 of file mrkiss_erk_kutta_4.f90.

  real(kind=rk),    parameter :: b(s,m) = reshape([ 1.0_rk, 2.0_rk, 2.0_rk, 1.0_rk], [s, m]) / 6.0_rk

c

real(kind=rk), dimension(s), parameter mrkiss_erk_kutta_4::c

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

Definition at line 75 of file mrkiss_erk_kutta_4.f90.

  real(kind=rk),    parameter :: c(s)   = [         0.0_rk, 1.0_rk, 1.0_rk, 2.0_rk]          / 2.0_rk

p

integer, dimension(m), parameter mrkiss_erk_kutta_4::p = [4]

The method orders.

Definition at line 77 of file mrkiss_erk_kutta_4.f90.

se

integer, dimension(m), parameter mrkiss_erk_kutta_4::se = [4]

Number of stages for each method.

Definition at line 79 of file mrkiss_erk_kutta_4.f90.