Comparative Numerical Evaluation of Some Runge-Kutta Methods for Solving First Order Systems of ODEs

Year 2025, Volume: 03, 20 - 28

Khadeejah James Audu , Tunde Adekunle Abubakar , Yahaya Yusuph Amuda , James Essien Nkereuwem

https://doi.org/10.54709/joebs.1556269

Abstract

In this study, a comparative analysis of two Runge-Kutta methods; fourth-order Runge-Kutta method and Butcher’s Fifth Order Runge-Kutta method are presented and used to solve systems of first-order linear Ordinary Differential Equations (ODEs). The main interest of this work is to test the accuracy, convergence rate and computational efficiency of these methods by using different numerical problems of ODEs. Empirical conclusions are drawn after close observation of the results presented by the two methods, which further highlights their limitations and enabling researchers to make informed decisions in choosing the appropriate technique for specific systems of ODEs problems.

Keywords

Runge-Kutta Methods, First Order ODEs, Numerical Methods, Convergence rate, Numerical Analysis

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