Title: Algorithms of algebraic order nine for numerically solving second-order boundary and initial value problems in ordinary differential equations

Authors: Ezekiel Olaoluwa Omole; Friday Oghenerukevwe Obarhua; Adefunke Bosede Familua; Ali Shokri

Addresses: Department of Mathematics and Statistics, College of Natural Sciences, Joseph Ayo Babalola University, Ikeji Arakeji, Osun State, Nigeria ' Department of Mathematical Sciences, School of Physical Sciences, The Federal University of Technology, Akure, Ondo State, Nigeria ' Department of Mathematics and Statistics, First-Technical University Ibadan, Oyo State, Nigeria ' Department of Mathematics, University of Maragheh, Maragheh, Iran

Abstract: A new numerical algorithm comprising of two-step with six off-step points is presented in this paper. The new method adopted interpolation of the approximate solution and collocation of the differential system in the development of the methods. The main method and its supplementary methods are combined to form the required integrators which are self-starting in nature. The implementation strategy is discussed and the new method has an algebraic order nine with significant properties that vindicate its effectiveness when applied to solve some standard second-order initial and boundary problems of ordinary differential equations such as nonlinear problem, variable coefficient problem, stiff problem, two body problem, Classical nonlinear Bratu's BVP in one-dimensional planar coordinates, Troesch's problem, Michaelis-Menten oxygen diffusion problem with uptake kinetic and the van der Pol oscillatory problem. The comparison of the new methods with some already existing methods confirmed that the method gives better accuracy. The effectiveness and efficiency are also demonstrated in the curves.

Keywords: two-step algorithms; ninth order algebraic methods; second order initial and boundary value problem; Michaelis-Menten oxygen diffusion problem; van der Pol oscillatory problem; Bratu's BVP in one-dimensional planar coordinates.

DOI: 10.1504/IJMOR.2023.132482

International Journal of Mathematics in Operational Research, 2023 Vol.25 No.3, pp.343 - 368

Received: 28 Dec 2021
Accepted: 16 Apr 2022
Published online: 24 Jul 2023 *

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