mrkiss_eerk_heun_euler_2_1 Module Reference

Butcher tableau for Heun & Euler 2 step, order (2,1) Runge-Kutta method. More...

Variables
integer, parameter	s = 2
	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 = [2, 1]
	The method orders.
integer, dimension(m), parameter	se = [2, 1]
	Number of stages for each method.

Detailed Description

Butcher tableau for Heun & Euler 2 step, order (2,1) Runge-Kutta method.

IMO

Included for historical reasons.

Known Aliases

• Overall method: 'RK21' (Butcher), 'ARKODE_HEUN_EULER_2_1_2' (SUNDIALS)
• First method: 'the trapezoidal rule', 'explicit trapezoidal rule', heun2, SSPRK2
• Second method: 'mrkiss_erk_euler_1' (MRKISS)

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_eerk_heun_euler_2_1::s = 2

The order of the overall method.

Definition at line 63 of file mrkiss_eerk_heun_euler_2_1.f90.

m

integer, parameter mrkiss_eerk_heun_euler_2_1::m = 2

Number of methods.

Definition at line 65 of file mrkiss_eerk_heun_euler_2_1.f90.

a

real(kind=rk), dimension(s,s), parameter mrkiss_eerk_heun_euler_2_1::a

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

Definition at line 67 of file mrkiss_eerk_heun_euler_2_1.f90.

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

b

real(kind=rk), dimension(s,m), parameter mrkiss_eerk_heun_euler_2_1::b

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

Definition at line 70 of file mrkiss_eerk_heun_euler_2_1.f90.

c

real(kind=rk), dimension(s), parameter mrkiss_eerk_heun_euler_2_1::c

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

Definition at line 73 of file mrkiss_eerk_heun_euler_2_1.f90.

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

p

integer, dimension(m), parameter mrkiss_eerk_heun_euler_2_1::p = [2, 1]

The method orders.

Definition at line 75 of file mrkiss_eerk_heun_euler_2_1.f90.

se

integer, dimension(m), parameter mrkiss_eerk_heun_euler_2_1::se = [2, 1]

Number of stages for each method.

Definition at line 77 of file mrkiss_eerk_heun_euler_2_1.f90.