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

Abhishek Das and Srinivasan Natesan

Applied Mathematics and Computation, 2015, vol. 271, issue C, 168-186

Abstract: 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.

Keywords: Singularly perturbed delay parabolic convection–diffusion problems; Boundary layers; Finite difference scheme; Piecewise-uniform Shishkin meshes; Uniform convergence (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:271:y:2015:i:c:p:168-186

DOI: 10.1016/j.amc.2015.08.137

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