Title: A continuous five-step implicit block unification method for numerical solution of second-order elliptic partial differential equations

Authors: Emmanuel Oluseye Adeyefa; Ezekiel Olaoluwa Omole

Addresses: Department of Mathematics, Faculty of Science, Federal University Oye-Ekiti, Ekiti State, Nigeria ' Department of Mathematics, Faculty of Science, Federal University Oye-Ekiti, Ekiti State, Nigeria

Abstract: A continuous implicit block unification method (CIBUM) is developed through the interpolation and collocation approach using Hermite polynomial as the basis function. The method is chosen within the interval of step-number of five. The basis function was interpolated at the first two consecutive points while the collocation was done at all the points within the interval of integration. The discrete scheme and their corresponding first derivative were combined to form the five-step implicit block unification method (FIBUM) of order six. The FIBUM is applied to solve second-order elliptic partial differential equations via the method of lines by transforming the PDEs into ODEs. The basic properties of FIBUM were investigated and found to be convergence and p-stable. The method was implemented on five test problems varying from linear, nonlinear, and nonlinear Klein-Gordon differential equations, and the results were presented. The results established the accuracy of the FIBUM over the existing ones.

Keywords: implicit block unification method; method of lines; second-order elliptic PDEs; convergence; Hermite polynomial; initial and boundary value problems; nonlinear Klein-Gordon differential equations.

DOI: 10.1504/IJMOR.2023.129482

International Journal of Mathematics in Operational Research, 2023 Vol.24 No.3, pp.360 - 386

Received: 10 Dec 2021
Accepted: 05 Feb 2022
Published online: 10 Mar 2023 *

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