Title: Development of a block method for solving multiple order ODEs

Authors: Emmanuel Oluseye Adeyefa; Adewale Adeyemi James; Adeyemi Sunday Olagunju; Folake Lois Joseph

Addresses: Mathematics Department, Federal University Oye-Ekiti, Nigeria ' Mathematics Department, American University of Nigeria, Yola, Nigeria ' Mathematics Department, Federal University of Lafia, Nigeria; Department of Mathematical Sciences, Bingham University, Karu, Nigeria ' Department of Mathematical Sciences, Bingham University, Karu, Nigeria

Abstract: In this work, a convergent hybrid block method (CHBM) with two off-grid points for direct integration of first, second, and third-order initial value problems (IVPs) is proposed. The development of a block method for the solution of IVPs has been considered overwhelmingly in the literature. However, using a block method to directly solve multi-order IVPs has not been so common. Thus, the formulation of a single numerical algorithm for the direct numerical integration of first, second and third-order IVPs is our focus. The method is formulated from a continuous scheme derived using collocation and interpolation techniques and implemented in a block-by-block manner as a numerical integrator for IVPs. To assess the method's applicability, efficiency, and accuracy, the convergence analysis has been investigated, and six test problems are considered.

Keywords: block method; collocation; convergence; interpolation; multiple order ODEs.

DOI: 10.1504/IJMOR.2024.141473

International Journal of Mathematics in Operational Research, 2024 Vol.29 No.1, pp.51 - 65

Received: 18 Jul 2022
Accepted: 07 Jan 2023
Published online: 16 Sep 2024 *

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