mrkiss_erk_midpoint_2 Module Reference

Butcher tableau for midpoint 2 step, order (2) Runge-Kutta method. More...

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

Detailed Description

Butcher tableau for midpoint 2 step, order (2) Runge-Kutta method.

IMO

Included for historical reasons.

Known Aliases

'RK22' (Butcher), 'midpoint method', 'the modpoint rule', 'Explicit midpoint method', 'Runge-2', 'R2'

Stability Image Links

References:

• Butcher (2016); Numerical Methods for Ordinary Differential Equations. 3ed; p98-99; zotero://select/items/0_V7UTIRPT

Variable Documentation

s

integer, parameter mrkiss_erk_midpoint_2::s = 2

The order of the overall method.

Definition at line 61 of file mrkiss_erk_midpoint_2.f90.

m

integer, parameter mrkiss_erk_midpoint_2::m = 1

Number of methods.

Definition at line 63 of file mrkiss_erk_midpoint_2.f90.

a

real(kind=rk), dimension(s,s), parameter mrkiss_erk_midpoint_2::a

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

Definition at line 65 of file mrkiss_erk_midpoint_2.f90.

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

b

real(kind=rk), dimension(s,m), parameter mrkiss_erk_midpoint_2::b

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

Definition at line 68 of file mrkiss_erk_midpoint_2.f90.

  real(kind=rk),    parameter :: b(s,m) = reshape([ 0.0_rk,  1.0_rk], [s, m]) / 1.0_rk

c

real(kind=rk), dimension(s), parameter mrkiss_erk_midpoint_2::c

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

Definition at line 70 of file mrkiss_erk_midpoint_2.f90.

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

p

integer, dimension(m), parameter mrkiss_erk_midpoint_2::p = [2]

The method orders.

Definition at line 72 of file mrkiss_erk_midpoint_2.f90.

se

integer, dimension(m), parameter mrkiss_erk_midpoint_2::se = [2]

Number of stages for each method.

Definition at line 74 of file mrkiss_erk_midpoint_2.f90.