Butcher tableau for Sofroniou Spaletta's 5 step, order (4,3) Runge-Kutta method. More...

Variables
integer, parameter	s = 5
	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, 3]
	The method orders.
integer, dimension(m), parameter	se = [4, 5]
	Number of stages for each method.

Detailed Description

Butcher tableau for Sofroniou Spaletta's 5 step, order (4,3) Runge-Kutta method.

IMO: This is an interesting method in that one of the goals was to detect stiffness. That said, it's a very good general purpose method of order 4.

Known Aliases: 'ARKODE_SOFRONIOU_SPALETTA_5_3_4' (SUNDIALS)

Stability Image Links

References:

Sofroniou & Spaletta (2004); Construction of Explicit Runge-Kutta Pairs with Stiffness Detection; Math. and Comp. Modelling; 40(11); p1157-1169; zotero://select/items/0_52X4WPJK

Variable Documentation

◆ s

integer, parameter mrkiss_eerk_sofroniou_spaletta_4_3::s = 5

The order of the overall method.

Definition at line 63 of file mrkiss_eerk_sofroniou_spaletta_4_3.f90.

◆ m

integer, parameter mrkiss_eerk_sofroniou_spaletta_4_3::m = 2

Number of methods.

Definition at line 65 of file mrkiss_eerk_sofroniou_spaletta_4_3.f90.

◆ a

real(kind=rk), dimension(s,s), parameter mrkiss_eerk_sofroniou_spaletta_4_3::a

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

Definition at line 67 of file mrkiss_eerk_sofroniou_spaletta_4_3.f90.

  real(kind=rk),    parameter :: a(s,s) = reshape([      0.0_rk,        0.0_rk,       0.0_rk,       0.0_rk,        0.0_rk, &
                                                      1584.0_rk,        0.0_rk,       0.0_rk,       0.0_rk,        0.0_rk, &
                                                      -594.0_rk,     2970.0_rk,       0.0_rk,       0.0_rk,        0.0_rk, &
                                                      1710.0_rk,    -1350.0_rk,    3600.0_rk,       0.0_rk,        0.0_rk, &
                                                       605.0_rk,     1375.0_rk,    1375.0_rk,     605.0_rk,        0.0_rk], [s, s]) /    3960.0_rk