Uniformly convergent hybrid numerical scheme for singularly perturbed delay parabolic convection–diffusion problems on Shishkin mesh

• Published in: Applied mathematics and computation Vol. 271; pp. 168 - 186
• Main Authors: Das, Abhishek, Natesan, Srinivasan
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.11.2015
• Subjects: Boundary layers; Finite difference scheme; Piecewise-uniform Shishkin meshes; Singularly perturbed delay parabolic convection–diffusion problems; Uniform convergence; Finite difference scheme; Uniform convergence; Piecewise-uniform Shishkin meshes; 65M06; CR G1.8; 65M12; Singularly perturbed delay parabolic convection–diffusion problems; Boundary layers
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2015.08.137

This article studies the numerical solution of singularly perturbed delay parabolic convection–diffusion initial-boundary-value problems. Since the solution of these problems exhibit regular boundary layers in the spatial variable, we use the piecewise-uniform Shishkin mesh for the discretization of the domain in the spatial direction, and uniform mesh in the temporal direction. The time derivative is discretized by the implicit-Euler scheme and the spatial derivatives are discretized by the hybrid scheme. For the proposed scheme, the stability analysis is carried out, and parameter-uniform error estimates are derived. Numerical examples are presented to show the accuracy and efficiency of the proposed scheme.