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

Modiu A. Mohammed, Johnson F. Baiyeri, Olayinka M. Ayeni, Ismaila S. Amusa and Temitope O. Ogunbayo
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Modiu A. Mohammed: Department of Mathematics, Yaba College of Technology, P.M.B. 2011, Yaba, Lagos, Nigeria
Johnson F. Baiyeri: Department of Mathematics, Yaba College of Technology, P.M.B. 2011, Yaba, Lagos, Nigeria
Olayinka M. Ayeni: Department of Mathematics, Yaba College of Technology, P.M.B. 2011, Yaba, Lagos, Nigeria
Ismaila S. Amusa: Department of Mathematics, Yaba College of Technology, P.M.B. 2011, Yaba, Lagos, Nigeria
Temitope O. Ogunbayo: Department of Mathematics, Yaba College of Technology, P.M.B. 2011, Yaba, Lagos, Nigeria

International Journal of Research and Innovation in Applied Science, 2023, vol. 8, issue 6, 94-108

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.

Date: 2023
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