mrkiss_erk_ralston_3 Module Reference

Butcher tableau for ralston's 3 stage order (3) Runge-Kutta method. 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 ralston's 3 stage order (3) Runge-Kutta method.

IMO

This method was designed to minimize truncation error over every other consideration includeing stability, roundoff error, performance, and storage.

Stability Image Links

References:

• Ralston (1962); Runge-Kutta Methods with Minimum Error Bounds; Math. of Comp. 16 (80); p431-437; zotero://select/items/0_2FK7F4J3

Variable Documentation

s

integer, parameter mrkiss_erk_ralston_3::s = 3

The order of the overall method.

Definition at line 60 of file mrkiss_erk_ralston_3.f90.

m

integer, parameter mrkiss_erk_ralston_3::m = 1

Number of methods.

Definition at line 62 of file mrkiss_erk_ralston_3.f90.

a

real(kind=rk), dimension(s,s), parameter mrkiss_erk_ralston_3::a

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

Definition at line 64 of file mrkiss_erk_ralston_3.f90.

  real(kind=rk),    parameter :: a(s,s) = reshape([ 0.0_rk, 0.0_rk, 0.0_rk, &
                                                    2.0_rk, 0.0_rk, 0.0_rk, &
                                                    0.0_rk, 3.0_rk, 0.0_rk], [s, s]) / 4.0_rk

b

real(kind=rk), dimension(s,m), parameter mrkiss_erk_ralston_3::b

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

Definition at line 68 of file mrkiss_erk_ralston_3.f90.

  real(kind=rk),    parameter :: b(s,m) = reshape([ 2.0_rk, 3.0_rk, 4.0_rk], [s, m]) / 9.0_rk

c

real(kind=rk), dimension(s), parameter mrkiss_erk_ralston_3::c

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

Definition at line 70 of file mrkiss_erk_ralston_3.f90.

  real(kind=rk),    parameter :: c(s)   = [         0.0_rk, 2.0_rk, 3.0_rk]          / 4.0_rk

p

integer, dimension(m), parameter mrkiss_erk_ralston_3::p = [3]

The method orders.

Definition at line 72 of file mrkiss_erk_ralston_3.f90.

se

integer, dimension(m), parameter mrkiss_erk_ralston_3::se = [3]

Number of stages for each method.

Definition at line 74 of file mrkiss_erk_ralston_3.f90.