Work

Numerical Solution of Fractional Singular Perturbation Cauchy Problem

Year: 2025

Type: article

Abstract: In this work, we consider a singularly perturbed Cauchy problem where the small parameter $ \varepsilon $ appears in the highest-order derivative term (i.e., the fractional derivative). First, we analyze some properties of the fractional singular perturbation problem. Then, a Shishkin mesh is introduced to address it, as traditional numerical methods for singularly perturbed problems may lead to numerical instability. Finally, we present numerical results demonstrating good stability and accuracy.

Source: Journal of Applied Analysis & Computation

DOI: 10.11948/20250018

Authors: Guocai Cai, Qingxia Liu

Institution: Xiamen University

Language: English

Topic: Differential Equations and Numerical Methods

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Natural Science Foundation of China, Natural Science Foundation of Fujian Province

Awards: G6335531314, G7949172245, G8532141224