Work

A new parameter-convergent nonstandard finite difference method for two-parameter singularly perturbed problems

Year: 2025

Type: article

Abstract: This article focuses on the numerical solution of a time-dependent parabolic problem that exhibits singular perturbations and involves two perturbation parameters. To address this problem, a fitted mesh finite difference method is developed. In numerical discretization, the implicit Crank-Nicolson technique is employed to discretize the time derivative using a uniform mesh. As for the spatial derivative, a hybrid finite difference scheme known as the adaptive fitted mesh of the Shishkin type is utilized. The study also includes a discussion on a priori bounds for the continuous solution and its derivatives. The proposed method is proven to be uniformly convergent of order two in both time and space. Theoretical analysis and simulations on various test examples confirm the scheme’s accuracy and convergence properties.

Source: Discover Applied Sciences

DOI: 10.1007/s42452-025-07721-8

Authors: Mekashaw Ali Mohye, Justin B. Munyakazi, Tekle Gemechu Dinka, Yusuf Hussen Haji, Abe Nura Ware, Jemal Muhammed Ahmed

Institutions: Wolkite University, Oda Bultum University, University of the Western Cape, Adama Science and Technology University, Arsi University

Language: English

Topic: Differential Equations and Numerical Methods

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4415376477

FWCI:

Cites: 24

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