Work

A uniformly accurate hybrid difference approximation of a system of singularly perturbed reaction-diffusion equations with delay using grid equidistribution

Year: 2026

Type: article

Abstract: This paper presents a uniformly accurate difference approximation for a system of singularly perturbed reaction-diffusion equations with delay. The proposed method utilizes an appropriate combination of exponential and cubic spline difference schemes. It employs grid equidistribution to address the challenges posed by the multiscale nature of these systems, which often feature sharp gradients and boundary layers. The grid is generated based on the equidistribution of a positive monitor function, a linear combination of a constant floor and a power of the second derivative of the solution. By using adaptive mesh generation and a spline difference method, the approach enhances the accuracy of the numerical solutions while maintaining computational efficiency. Numerical experiments validate the uniform convergence and theoretical findings, demonstrating the method’s robustness irrespective of the perturbation parameter size.

Source: Mathematical Modelling and Analysis

DOI: 10.3846/mma.2026.22256

Authors: Aditya Kaushik, Shivani Jain, Manju Sharma

Institutions: Delhi Technological University, University of Delhi, Indraprastha College for Women

Language: English

Topic: Differential Equations and Numerical Methods

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Science and Engineering Research Board

Award: G194302888