A uniformly convergent scheme to solve two‐dimensional parabolic singularly perturbed systems of reaction‐diffusion type with multiple diffusion parameters. Issue 3 (7th April 2020)

• Record Type: Journal Article
• Authors: Clavero, Carmelo; Jorge, Juan Carlos
• Is Part Of: Computational and mathematical methods. Volume 3:Issue 3(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2020-04-07
• Subjects: fractional Euler method -- reaction‐diffusion parabolic systems -- Shishkin meshes -- splitting by components -- uniform convergence; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Periodicals; Numerical analysis; Mathematics -- Data processing; Periodicals; 004.0151
• DOI: 10.1002/cmm4.1093
• Languages: English
• ISSNs: 2577-7408

Abstract

Abstract : In this work, we deal with solving two‐dimensional parabolic singularly perturbed systems of reaction‐diffusion type where the diffusion parameters at each equation of the system can be small and of different scale. In such case, in general, overlapping boundary layers appear at the boundary of the spatial domain and, because of this, special meshes are required to resolve them. The numerical scheme combines the central difference scheme to discretize in space and the fractional implicit Euler method together with a splitting by components to discretize in time. If the fully discrete scheme is defined on an adequate piecewise uniform Shishkin mesh in space then it is uniformly convergent of first order in time and of almost second order in space. Some numerical results illustrate the theoretical results.