Uniformly Convergent Numerical Method for Singularly Perturbed Two Parameter Time Delay Parabolic Problem

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...

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Bibliographic Details
Published in:International journal of applied and computational mathematics 2019-06, Vol.5 (3), p.1-9, Article 91
Main Authors: Govindarao, L., Mohapatra, J., Sahu, S. R.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Applied mathematics
Computational mathematics
Computational Science and Engineering
Convection
Convergence
Discretization
Mathematical and Computational Physics
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Nuclear Energy
Numerical methods
Operations Research/Decision Theory
Original Paper
Parameters
Recent Advances in Mathematics and its Applications
Singular perturbation methods
Theoretical
Time lag
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Summary: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.
ISSN:2349-5103
2199-5796
DOI:10.1007/s40819-019-0672-5