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A second order numerical method for singularly perturbed delay parabolic partial differential equation

Publication Type : Journal Article

Publisher : Emerald Publishing Limited

Source : Emerald Publishing Limited

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 a robust second-order numerical scheme for singularly perturbed delay parabolic convection–diffusion initial boundary value problem. Design/methodology/approach For the parabolic convection-diffusion initial boundary value problem, the authors solve the problem numerically by discretizing the domain in the spatial direction using the Shishkin-type meshes (standard Shishkin mesh, Bakhvalov–Shishkin mesh) and in temporal direction using the uniform mesh. The time derivative is discretized by the implicit-trapezoidal scheme, and the spatial derivatives are discretized by the hybrid scheme, which is a combination of the midpoint upwind scheme and central difference scheme. Findings The authors find a parameter-uniform convergent scheme which is of second-order accurate globally with respect to space and time for the singularly perturbed delay parabolic …

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