Numerical Analysis of Singularly Perturbed System of Parabolic Convection–Diffusion Problem with Regular Boundary Layers

• Published in: Differential equations and dynamical systems Vol. 30; no. 3; pp. 695 - 717
• Main Authors: Singh, Maneesh Kumar, Natesan, Srinivasan
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01.07.2022; Springer Nature B.V
• Subjects: Boundary layers; Computer Science; Convection; Diffusion layers; Engineering; Error analysis; Finite difference method; Mathematics; Mathematics and Statistics; Numerical analysis; Original Research; Parameters; Perturbation; Stability analysis; Finite difference scheme; Uniform convergence; Singularly perturbed system; Shishkin mesh; AMS 65M06; CR G1.8; Parabolic convection–diffusion problems; 65M12; Boundary layers
• ISSN: 0971-3514; 0974-6870
• DOI: 10.1007/s12591-019-00462-2

In this article, we obtain the numerical solution of singularly perturbed system of parabolic convection–diffusion problems exhibiting boundary layer. The proposed numerical scheme consists of the backward-Euler method for the time derivative and an upwind finite difference scheme for the spatial derivatives. We analyze the scheme on a piecewise-uniform Shishkin mesh for the spatial discretization to establish uniform convergence with respect to the perturbation parameters. For the proposed scheme, the stability analysis is presented and parameter-uniform error estimate is derived. In order to validate the theoretical results, we have carried out some numerical experiments.