Author(s)

Georgios D. Trikkaliotis, Maria Ch. Gousidou-Koutita

Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki, Greece.

The purpose of the present work is to construct a nonlinear equation system (85 × 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^th 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.

Initial Value Problem, Runge-Kutta Methods, Ordinary Differential Equations

Trikkaliotis, G. and Gousidou-Koutita, M. (2022) Production of the Reduction Formula of Seventh Order Runge-Kutta Method with Step Size Control of an Ordinary Differential Equation. Applied Mathematics, 13, 325-337. doi: 10.4236/am.2022.134023.