mrkiss_eerk_cash_karp_5_4.f90 File Reference

Butcher tableau for Cash & Karp's 4 step, order (5,4) Runge-Kutta method. More...

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Modules
module	mrkiss_eerk_cash_karp_5_4
	Butcher tableau for Cash & Karp's 4 step, order (5,4) Runge-Kutta method.

Variables
integer, parameter	mrkiss_eerk_cash_karp_5_4::s = 6
	The order of the overall method.
integer, parameter	mrkiss_eerk_cash_karp_5_4::m = 5
	Number of methods.
real(kind=rk), dimension(s, s), parameter	mrkiss_eerk_cash_karp_5_4::a
	The \(\mathbf{a}\) matrix for the Butcher Tableau.
real(kind=rk), dimension(s, m), parameter	mrkiss_eerk_cash_karp_5_4::b
	The \(\mathbf{b}\) matrix for the Butcher Tableau.
real(kind=rk), dimension(s), parameter	mrkiss_eerk_cash_karp_5_4::c
	The \(\mathbf{c}\) matrix for the Butcher Tableau.
integer, dimension(m), parameter	mrkiss_eerk_cash_karp_5_4::p = [5, 4, 3, 2, 1]
	The method orders.
integer, dimension(m), parameter	mrkiss_eerk_cash_karp_5_4::se = [6, 6, 4, 2, 1]
	Number of stages for each method.

Detailed Description

Butcher tableau for Cash & Karp's 4 step, order (5,4) Runge-Kutta method.

Author

Mitch Richling http://www.mitchr.me/

Keywords

ode ivp differential equation initial value problem rk

Standards

F2023

See also

https://github.com/richmit/MRKISS

Copyright

Copyright (c) 2025, Mitchell Jay Richling http://www.mitchr.me/ All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

1. Redistributions of source code must retain the above copyright notice, this list of conditions, and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions, and the following disclaimer in the documentation and/or other materials provided with the distribution.
3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

Definition in file mrkiss_eerk_cash_karp_5_4.f90.