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

Publication Type : Journal Article

Publisher : Emerald

Source : Emerald

Campus : Coimbatore

School : School of Engineering

Center : Amrita Innovation & Research

Department : Mathematics

Verified : Yes

Year : 2019

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 …v

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