Production of the Reduction Formula of Seventh Order Runge-Kutta Method with Step Size Control of an Ordinary Differential Equation  

作　　者：Georgios D. Trikkaliotis Maria Ch. Gousidou-Koutita Georgios D. Trikkaliotis;Maria Ch. Gousidou-Koutita(Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki, Greece)

机构地区：[1]Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki, Greece

出　　处：《Applied Mathematics》2022年第4期325-337,共13页应用数学（英文）

摘　　要：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.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.

关 键 词：Initial Value Problem Runge-Kutta Methods Ordinary Differential Equations 

分 类 号：O241.8[理学—计算数学]