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Uniformly convergent numerical method for singularly perturbed two parameter time delay parabolic problem

Publication Type : Journal Article

Publisher : Springer India

Source : Springer India

Campus : Coimbatore

School : School of Engineering

Center : Amrita Innovation & Research

Department : Mathematics

Verified : Yes

Year : 2019

Abstract : This paper discusses the numerical solution of one dimensional parabolic convection–reaction–diffusion time delay problem with two small parameters. For the discretization of the time derivative, we use the implicit Euler scheme on a uniform mesh and for the spatial discretization, we use the upwind difference scheme on the Shishkin type meshes (standard Shishkin mesh, Bakhvalov–Shishkin mesh). We prove that numerically the proposed method is provides a first order convergence, which is optimal for this case. Finally, to support the theoretical results, we present some numerical experiments using the proposed method.

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