Butcher tableau for Bogacki Shampine's 4 step, order (3,2) Runge-Kutta method. More...

Variables
integer, parameter	s = 4
	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 = [3, 2]
	The method orders.
integer, dimension(m), parameter	se = [3, 4]
	Number of stages for each method.

Detailed Description

Butcher tableau for Bogacki Shampine's 4 step, order (3,2) Runge-Kutta method.

IMO: This is my go-to O(3) method.

Known Aliases: 'Shampine3' (OrdinaryDiffEq.jl), 'ode23' (MATLAB & Octave), 'ARKODE_BOGACKI_SHAMPINE_4_2_3' (SUNDIALS).

Stability Image Links

References:

Bogacki & Shampine (1989); A 3(2) pair of Runge-Kutta formulas; Applied Mathematics Letters; zotero://select/items/0_66MV7TIP

Variable Documentation

◆ s

integer, parameter mrkiss_eerk_bogacki_shampine_3_2::s = 4

The order of the overall method.

Definition at line 61 of file mrkiss_eerk_bogacki_shampine_3_2.f90.

◆ m

integer, parameter mrkiss_eerk_bogacki_shampine_3_2::m = 2

Number of methods.

Definition at line 63 of file mrkiss_eerk_bogacki_shampine_3_2.f90.

◆ a

real(kind=rk), dimension(s,s), parameter mrkiss_eerk_bogacki_shampine_3_2::a

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

Definition at line 65 of file mrkiss_eerk_bogacki_shampine_3_2.f90.

  real(kind=rk),    parameter :: a(s,s) = reshape([  0.0_rk,  0.0_rk,  0.0_rk, 0.0_rk, &
       &                                            18.0_rk,  0.0_rk,  0.0_rk, 0.0_rk, &
       &                                             0.0_rk, 27.0_rk,  0.0_rk, 0.0_rk, &
       &                                             8.0_rk, 12.0_rk, 16.0_rk, 0.0_rk], [s, s]) / 36.0_rk