Butcher tableau for Knoth & wolke's 3 stage Runge-Kutta method of O(3) More...

Variables
integer, parameter	s = 3
	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 = [3]
	The method orders.
integer, dimension(m), parameter	se = [3]
	Number of stages for each method.

Detailed Description

Butcher tableau for Knoth & wolke's 3 stage Runge-Kutta method of O(3)

IMO: Included for historical reasons.

Known Aliases: 'ARKODE_KNOTH_WOLKE_3_3' (SUNDIALS)

Stability Image Links

References:

Knoth & Wolke (1988); Implicit-explicit runge-kutta methods for computiong atmospheric reactive flows; Appl. Num. Anal; 28(2-4); p327-341

Variable Documentation

◆ s

integer, parameter mrkiss_erk_knoth_wolke_3::s = 3

The order of the overall method.

Definition at line 62 of file mrkiss_erk_knoth_wolke_3.f90.

◆ m

integer, parameter mrkiss_erk_knoth_wolke_3::m = 1

Number of methods.

Definition at line 64 of file mrkiss_erk_knoth_wolke_3.f90.

◆ a

real(kind=rk), dimension(s,s), parameter mrkiss_erk_knoth_wolke_3::a

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

Definition at line 66 of file mrkiss_erk_knoth_wolke_3.f90.

  real(kind=rk),    parameter :: a(s,s) = reshape([  0.0_rk,  0.0_rk, 0.0_rk, &
                                                    16.0_rk,  0.0_rk, 0.0_rk, &
                                                    -9.0_rk, 45.0_rk, 0.0_rk], [s, s]) / 48.0_rk