SJ Kayode¹*, FO Obarhua¹ and OS Ige²

¹Mathematical Science Department, Federal University of Technology Akure, Nigeria
²Department of Foundation Studies, Babcock University Ilishan-Remo, Nigeria

*Corresponding Author: SJ Kayode, Mathematical Science Department, Federal University of Technology Akure, Nigeria

Received: November 23, 2023; Published: November 30, 2023

Abstract

Our aim is to construct an implicit three step method with multiderivative to handle general second order initial value problems of ordinary differential equations (ODEs) directly. The study provides the use of both collocation and interpolation techniques to obtain the method. In deriving the method, power series and Bernstein polynomial in combine was used as an approximate solution. An order six, consistent, zero-stable method and hence convergent is obtained. The main predictor was developed using the same approach and is of equal order as the corrector. Absolute error of the method obtained with some test problems showed an improve accuracy over the existing methods in the reviewed literature.

Keywords: Second Order; Ordinary Differential Equation; Multi-derivative; Interpolation; Collocation; Predictor-Corrector; Consistency; Zero Stable

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Citation

Citation: SJ Kayode., et al. “Implicit Three-Step Multi-Derivative Algorithm for the Solution of Second Order Ordinary Differential Equations".Acta Scientific Computer Sciences 5.12 (2023): 14-20.

Copyright

Copyright: © 2023 SJ Kayode., et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.