mrkiss_erk_euler_1 Module Reference

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

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

Detailed Description

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

IMO

This algorithm is commonly used for strange attractors, and by some combined algorithms as an error estimator. I include it mostly for historical reasons.

Known Aliases

'The Euler Mmethod', 'Euler 1 step', 'RK1', 'Forward Euler', 'ARKODE_FORWARD_EULER_1_1' (SUNDIALS)

Stability Image Links

References:

• Euler (1768); Institutionum Calculi Integralis. Volumen Primum, Opera Omnia, Vol XI. p424
• Hairer, Norsett & Wanner (2009). Solving Ordinary Differential Equations. I: Nonstiff Problems. p35; zotero://select/items/0_VLZWN2CT
• Butcher (2016); Numerical Methods for Ordinary Differential Equations. 3ed; p98; zotero://select/items/0_V7UTIRPT

Variable Documentation

s

integer, parameter mrkiss_erk_euler_1::s = 1

The order of the overall method.

Definition at line 65 of file mrkiss_erk_euler_1.f90.

m

integer, parameter mrkiss_erk_euler_1::m = 1

Number of methods.

Definition at line 67 of file mrkiss_erk_euler_1.f90.

a

real(kind=rk), dimension(s,s), parameter mrkiss_erk_euler_1::a

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

Definition at line 69 of file mrkiss_erk_euler_1.f90.

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

b

real(kind=rk), dimension(s,m), parameter mrkiss_erk_euler_1::b

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

Definition at line 71 of file mrkiss_erk_euler_1.f90.

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

c

real(kind=rk), dimension(s), parameter mrkiss_erk_euler_1::c

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

Definition at line 73 of file mrkiss_erk_euler_1.f90.

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

p

integer, dimension(m), parameter mrkiss_erk_euler_1::p = [1]

The method orders.

Definition at line 75 of file mrkiss_erk_euler_1.f90.

se

integer, dimension(m), parameter mrkiss_erk_euler_1::se = [1]

Number of stages for each method.

Definition at line 77 of file mrkiss_erk_euler_1.f90.