Title: Single numerical algorithm developed to solving first and second orders ordinary differential equations

Authors: John Olusola Kuboye; Bamikole Gbenga Ogunware; Ezekiel Olusola Abolarin; Chika O. Mmaduakor

Addresses: Department of Mathematics, Federal University Oye-Ekiti, Ekiti State, Nigeria ' Mathematics and Statistics Department, Joseph Ayo Babalola University Ikeji-Arakeji, Osun State, Nigeria ' Department of Mathematics, Federal University Oye-Ekiti, Ekiti State, Nigeria ' Department of Mathematics, Federal University Oye-Ekiti, Ekiti State, Nigeria

Abstract: A potent numerical algorithm for solving first and second orders initial value problems is examined in this paper. Interpolation and collocation approach was applied in the derivation of the new method with the use of power series approximate solution as interpolating polynomial. The two numerical integrators that formed the block were derived by evaluating the non-interpolating points within the selected interval of integration. To examine the effectiveness of the block, it was tested on some first and second orders ordinary differential equations and results generated performed better when compared with existing methods in terms of accuracy.

Keywords: block method; collocation; hybrid; interpolation; power series; first order IVP; second order IVP.

DOI: 10.1504/IJMOR.2022.122805

International Journal of Mathematics in Operational Research, 2022 Vol.21 No.4, pp.466 - 479

Received: 18 Aug 2020
Accepted: 02 Feb 2021
Published online: 12 May 2022 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article