On New Runge-Kutta Second and Third Orders for Solving First Order ODE

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On New Runge-Kutta Second and Third Orders for Solving First Order ODE

Modiu A. MOHAMMED1; Johnson F. BAIYERI2; Olayinka M. AYENI 3; Ismaila S. AMUSA 4 and Temitope O. OGUNBAYO 5
12345Department of Mathematics, Yaba College of Technology, P.M.B. 2011, Yaba, Lagos, Nigeria
DOI: https://doi.org/10.51584/IJRIAS.2023.8612
Received: 01 June 2023; Accepted: 07 June 2023; Published: 07 July 2023

Abstract:- Runge-Kutta methods are iterative methods for the approximation of solutions of ODE’s that were developed around 1900 by the German Mathematicians C. Runge (1856–1927) and M.W. Kutta (1867–1944). Runge-Kutta methods provide a popular way to solve the initial value problem for a system of ordinary differential equations and many Mathematicians have developed these methods in different ways. In this research work, we gave the overview of Runge-Kutta second and third orders in a simplified way and obtained new Runge-Kutta methods for these orders; our new schemes are better than the previous results obtained on the method.

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I. Introduction

Runge-Kutta methods are part of the methods used in solving first order initial value problem of the form: