Butcher tableau for Fehlberg's 13 stage, Order (7,8) Runge-Kutta method. More...

Variables
integer, parameter	s = 13
	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 = [7, 8]
	The method orders.
integer, dimension(m), parameter	se = [11, 13]
	Number of stages for each method.

Detailed Description

Butcher tableau for Fehlberg's 13 stage, Order (7,8) Runge-Kutta method.

IMO: Included for historical reasons. Performs poorly in local extrapolation mode. This one was pretty broadly used, but not nearly as much as mrkiss_eerk_fehlberg_4_5. It was largely replaced by mrkiss_eerk_dormand_prince_7_8.

Known Aliases: 'RKF78'', 'ode78' (OrdinaryDiffEq.jl), 'ARKODE_FEHLBERG_13_7_8' (SUNDIALS).

References:

Erwin Fehlberg (1972); Classical eight- and lower-order Runge-Kutta-Nystroem formulas with stepsize control for special second-order differential equations; NASA Technical Report M-533
Butcher (2008); Numerical Methods for Ordinary Differential Equations. 2ed; p209; zotero://select/items/0_8V2GY73E
Butcher (2016); Numerical Methods for Ordinary Differential Equations. 3ed; p222; zotero://select/items/0_V7UTIRPT
Hairer, Norsett & Wanner (2009). Solving Ordinary Differential Equations. I: Nonstiff Problems. p180;