Butcher tableau for the three eights rule. 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 three eights rule.

A 4 step, order (4) Runge-Kutta method

IMO: Included for historical reasons. More precise than RK4.

Known Aliases: '3/8 rule', 'RK42' (Butcher), 'GIRK438' (OrdinaryDiffEq.jl).

Stability Image Links

References:

Kutta (1901), Beitrag zur n"herungsweisen Integration totaler Differentialgleichungen; Z. Math. Phys. 46; p435-453.
Hairer, Norsett & Wanner (2009). Solving Ordinary Differential Equations. I: Nonstiff Problems. p138; zotero://select/items/0_VLZWN2CT

Variable Documentation

◆ s

integer, parameter mrkiss_erk_kutta_three_eight_4::s = 4

The order of the overall method.

Definition at line 63 of file mrkiss_erk_kutta_three_eight_4.f90.

◆ m

integer, parameter mrkiss_erk_kutta_three_eight_4::m = 1

Number of methods.

Definition at line 65 of file mrkiss_erk_kutta_three_eight_4.f90.

◆ a

real(kind=rk), dimension(s,s), parameter mrkiss_erk_kutta_three_eight_4::a

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

Definition at line 67 of file mrkiss_erk_kutta_three_eight_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, &
                                                   -1.0_rk,  3.0_rk, 0.0_rk, 0.0_rk, &
                                                    3.0_rk, -3.0_rk, 3.0_rk, 0.0_rk], [s, s]) / 3.0_rk