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Numerical analysis and simulation of delay parabolic partial differential equation involving a small parameter

Lolugu Govindarao (Department of Mathematics, National Institute of Technology, Rourkela, India)
Jugal Mohapatra (Department of Mathematics, National Institute of Technology, Rourkela, India)

Engineering Computations

ISSN: 0264-4401

Article publication date: 27 August 2019

Issue publication date: 16 January 2020

Abstract

Purpose

The purpose of this paper is to provide an efficient and robust second-order monotone hybrid scheme for singularly perturbed delay parabolic convection-diffusion initial boundary value problem.

Design/methodology/approach

The delay parabolic problem is solved numerically by a finite difference scheme consists of implicit Euler scheme for the time derivative and a monotone hybrid scheme with variable weights for the spatial derivative. The domain is discretized in the temporal direction using uniform mesh while the spatial direction is discretized using three types of non-uniform meshes mainly the standard Shishkin mesh, the Bakhvalov–Shishkin mesh and the Gartland Shishkin mesh.

Findings

The proposed scheme is shown to be a parameter-uniform convergent scheme, which is second-order convergent and optimal for the case. Also, the authors used the Thomas algorithm approach for the computational purposes, which took less time for the computation, and hence, more efficient than the other methods used in literature.

Originality/value

A singularly perturbed delay parabolic convection-diffusion initial boundary value problem is considered. The solution of the problem possesses a regular boundary layer. The authors solve this problem numerically using a monotone hybrid scheme. The error analysis is carried out. It is shown to be parameter-uniform convergent and is of second-order accurate. Numerical results are shown to verify the theoretical estimates.

Keywords

Citation

Govindarao, L. and Mohapatra, J. (2020), "Numerical analysis and simulation of delay parabolic partial differential equation involving a small parameter", Engineering Computations, Vol. 37 No. 1, pp. 289-312. https://doi.org/10.1108/EC-03-2019-0115

Publisher

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Emerald Publishing Limited

Copyright © 2019, Emerald Publishing Limited