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ORIGINAL RESEARCH article

Front. Appl. Math. Stat.
Sec. Numerical Analysis and Scientific Computation
Volume 10 - 2024 | doi: 10.3389/fams.2024.1501271
This article is part of the Research Topic Advanced Numerical Methods for Solving Singularly Perturbed Differential Equations View all articles

A robust exponentially fitted higher order numerical method for a two parameter singularly perturbed boundary value problem

Provisionally accepted
Fasika Wondimu Gelu Fasika Wondimu Gelu 1,2*Adisie Fenta Agmas Adisie Fenta Agmas 2Meselech Chima Fino Meselech Chima Fino 1,2
  • 1 College of Natural and Computational Sciences, Dilla University, Dilla, Ethiopia
  • 2 Dilla University, Dilla, SNNPR, Ethiopia

The final, formatted version of the article will be published soon.

    This study constructs a robust higher order fitted operator finite difference method for a two parameter singularly perturbed boundary value problem. The derivatives in the governing ordinary differential equation are substituted by second order central finite difference approximations, after which the fitting parameter is introduced and determined. The resulting system of linear equations may then be solved using the Thomas method. The current method's stability, consistency, and convergence have been thoroughly tested. To increase accuracy and provide a higher order numerical solution, a post-processing technique was used to accelerate the second order convergent method to the fourth order convergent method. Finally, three test examples are used to confirm the method's appropriateness. The numerical results demonstrate that the proposed technique is stable, consistent, and produces a higher-order numerical solution than the previous ones in the literature.

    Keywords: An exponentially fitted, Higher order method, two parameters, Post-processing technique, Twin boundary layers

    Received: 24 Sep 2024; Accepted: 04 Dec 2024.

    Copyright: © 2024 Gelu, Agmas and Fino. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

    * Correspondence: Fasika Wondimu Gelu, College of Natural and Computational Sciences, Dilla University, Dilla, Ethiopia

    Disclaimer: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.