A hybrid simulation for a system of singularly perturbed two-point reaction-diffusion equations

TL;DR

This paper introduces a hybrid numerical-asymptotic method combining SCEM and finite differences to efficiently solve singularly perturbed reaction-diffusion systems, demonstrated through illustrative examples.

Contribution

It presents a novel hybrid approach that integrates asymptotic and numerical techniques for solving complex reaction-diffusion equations with singular perturbations.

Findings

The method shows high efficiency in solving the systems.

It demonstrates good convergence properties.

The approach is easy to apply to practical problems.

Abstract

This study concerns with singularly perturbed systems of second-order reaction-diffusion equations in ODE's. To handle this type of problems, a numerical-asymptotic hybrid method is employed. In this hybrid method, an efficient asymptotic method, the so-called Successive complementary expansion method (SCEM) is applied first and then, a numerical method based on finite differences is proposed to approximate the solution of the corresponding singularly perturbed reaction-diffusion systems. Two illustrative examples are provided to show the efficiency and easy-applicability of the present method with convergence properties.