A robust fitted finite difference method for semi-linear two-parameter singularly perturbed PDEs

Mohye, Mekashaw Ali; Munyakazi, Justin B.; Dinka, Tekle Gemechu; Haji, Yusuf Hussen; Ware, Abe NUra; Ahmed, Jemal Muhammed

doi:10.22124/jmm.2025.30916.2776

A robust fitted finite difference method for semi-linear two-parameter singularly perturbed PDEs

Articles in Press

Document Type : Research Article

Authors

¹ Department of Mathematics, College of Natural and Computational Science, Wolkite University, Wolkite, Ethiopia

² Department of Mathematics and Applied Mathematics University of Western Cape

³ Department of Applied Mathematics Adama Science and Technology University

⁴ Department of Mathematics, Arsi University, Asela, Ethiopia

⁵ Department of Mathematics, Oda Bultum University, Chiro, Ethiopia

10.22124/jmm.2025.30916.2776

Abstract

In this article, a new numerical approach is developed for nonlinear two-parameter singularly perturbed initial-boundary value problems. The implicit backward Euler discretization for the time derivative and the fitted operator technique in the spatial domain are employed. Newton's quasilinearization technique is applied to the nonlinear terms. An investigation of parameter-uniform error estimates shows that the developed approach is first-order accurate in both time and space. However, a temporal mesh refinement technique is introduced to improve the order of accuracy to two. Two examples are provided and implemented in Python to validate the applicability of the method, and the results are displayed in tables and graphs.

Keywords

Main Subjects