%0 Journal Article
%T Production of the Reduction Formula of Seventh Order Runge-Kutta Method with Step Size Control of an Ordinary Differential Equation
%A Georgios D. Trikkaliotis
%A Maria Ch. Gousidou-Koutita
%J Applied Mathematics
%P 325-337
%@ 2152-7393
%D 2022
%I Scientific Research Publishing
%R 10.4236/am.2022.134023
%X The purpose of the present work is to construct a nonlinear equation system (85 ¡Á 53) using Butcher¡¯s Table and then by solving this system to find the values of all set parameters and finally the reduction formula of the Runge-Kutta (7,9) method (7<sup>th</sup> order and 9 stages) for the solution of an Ordinary Differential Equation (ODE). Since the system of high order conditions required to be solved is too complicated, we introduce a subsystem from the original system where all coefficients are found with respect to 9 free parameters. These free parameters, as well as some others in addition, are adjusted in such a way to furnish more efficient R-K methods. We use the MATLAB software to solve several of the created subsystems for the comparison of our results which have been solved analytically.
%K Initial Value Problem
%K Runge-Kutta Methods
%K Ordinary Differential Equations
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=116803