Efficient component-wise splitting approach to solve coupled singularly perturbed parabolic reaction-diffusion systems with interior layers

Jaiswal, Aishwarya ; Kumar, Sunil ; Clavero, Carmelo (Universidad de Zaragoza)

Resumen: In this work, our goal is to construct an efficient numerical approach to solve one dimensional parabolic linear singularly perturbed reaction-diffusion systems, for which the source term of the differential equation has a jump discontinuity at an interior point of the spatial domain. The diffusion parameters, which appear at each equation of the system, can be distinct and also they can have a different order of magnitude. Then, in general, overlapping parabolic boundary layers appear at both end points of the spatial interval, along with overlapping interior layers at the point of discontinuity. The method to tackle the considered problem, combines a special finite difference scheme at the point of discontinuity and the classical central finite difference scheme at other points, defined on a piecewise uniform Shishkin mesh, to discretize in space, together with the fractional implicit Euler approach with a component-wise splitting, defined on a uniform mesh, to discretize in time. Then, the fully discrete algorithm reduces the computational cost challenge for this kind of problems by decoupling the components of the discrete solution, because only tridiagonal linear systems must be solved at each discrete time step. The numerical scheme is a uniformly convergent method with first order accuracy in time and almost second order in space. Some test problems are solved by using our numerical algorithm; the numerical results obtained corroborate in practice the predicted outcomes and also the computational efficiency of the proposed technique.

Idioma: Inglés

DOI: 10.1007/s11075-025-02133-6

Año: 2025

Publicado en: NUMERICAL ALGORITHMS (2025), [29 pp.]
ISSN: 1017-1398

Financiación: info:eu-repo/grantAgreement/ES/DGA/E24-17R
Financiación: info:eu-repo/grantAgreement/ES/MINECO/MTM2017-83490-P

Tipo y forma: Artículo (PostPrint)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)