Work

A Non-Standard Finite Difference Scheme for Time-Fractional Singularly Perturbed Convection–Diffusion Problems

Year: 2025

Type: article

Abstract: This paper introduces a stable non-standard finite difference (NSFD) method to solve time-fractional singularly perturbed convection–diffusion problems. The fractional derivative in time is defined in the Caputo sense. The proposed method shows high efficiency when applied using a uniform mesh and can be easily extended to a Shishkin mesh in the spatial domain. We discuss error estimates to demonstrate the convergence of the numerical scheme. Additionally, various numerical examples are presented to illustrate the behavior of the solution for different values of the perturbation parameter ϵ and the order of the fractional derivative.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract9060333

Authors: Pramod Chakravarthy Podila, Rahul Mishra, Higinio Ramos

Institutions: Visvesvaraya National Institute of Technology, Universidad de Salamanca

Language: English

Topic: Differential Equations and Numerical Methods

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,258

OpenAlex ID: W4410628544

FWCI: 3.212

Cites: 28

Cited by: 3

Related to: 10