research-article

High order parameter-uniform discretization for singularly perturbed parabolic partial differential equations with time delay

Authors:

Mukesh KumarAuthors Info & Claims

Computers & Mathematics with Applications, Volume 68, Issue 10

Pages 1355 - 1367

https://doi.org/10.1016/j.camwa.2014.09.004

Published: 01 November 2014 Publication History

Abstract

In this article we study numerical approximation for singularly perturbed parabolic partial differential equations with time delay. A priori bounds on the exact solution and its derivatives, which are useful for the error analysis of the numerical method are given. The problem is discretized by a hybrid scheme on a generalized Shishkin mesh in spatial direction and the implicit Euler scheme on a uniform mesh in time direction. We then design a Richardson extrapolation scheme to increase the order of convergence in time direction. The resulting scheme is proved to be second order accurate in time direction and fourth order (with a factor of logarithmic type) accurate in spatial direction. Numerical experiments are performed to support the theoretical results.

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Cited By

Kumar SKumar SSumit (2024)A priori and a posteriori error estimation for singularly perturbed delay integro-differential equationsNumerical Algorithms10.1007/s11075-023-01620-y95:4(1561-1582)Online publication date: 1-Apr-2024
https://dl.acm.org/doi/10.1007/s11075-023-01620-y
Babu GPrithvi MSharma KRamesh V(2022)A robust numerical algorithm on harmonic mesh for parabolic singularly perturbed convection-diffusion problems with time delayNumerical Algorithms10.1007/s11075-022-01275-191:2(615-634)Online publication date: 1-Oct-2022
https://dl.acm.org/doi/10.1007/s11075-022-01275-1
Zhang YGuo JQiu BLi W(2019)Zhang Neural Dynamics Approximated by Backward Difference Rules in Form of Time-Delay Differential EquationNeural Processing Letters10.1007/s11063-018-9956-850:2(1735-1753)Online publication date: 1-Oct-2019
https://dl.acm.org/doi/10.1007/s11063-018-9956-8
Show More Cited By

High order parameter-uniform discretization for singularly perturbed parabolic partial differential equations with time delay
1. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
2. Theory of computation

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cover image Computers & Mathematics with Applications

Computers & Mathematics with Applications Volume 68, Issue 10

November 2014

396 pages

ISSN:0898-1221

Issue’s Table of Contents

Copyright © Elsevier Ltd.

Publisher

Pergamon Press, Inc.

United States

Publication History

Published: 01 November 2014

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Cited By

Kumar SKumar SSumit (2024)A priori and a posteriori error estimation for singularly perturbed delay integro-differential equationsNumerical Algorithms10.1007/s11075-023-01620-y95:4(1561-1582)Online publication date: 1-Apr-2024
https://dl.acm.org/doi/10.1007/s11075-023-01620-y
Babu GPrithvi MSharma KRamesh V(2022)A robust numerical algorithm on harmonic mesh for parabolic singularly perturbed convection-diffusion problems with time delayNumerical Algorithms10.1007/s11075-022-01275-191:2(615-634)Online publication date: 1-Oct-2022
https://dl.acm.org/doi/10.1007/s11075-022-01275-1
Zhang YGuo JQiu BLi W(2019)Zhang Neural Dynamics Approximated by Backward Difference Rules in Form of Time-Delay Differential EquationNeural Processing Letters10.1007/s11063-018-9956-850:2(1735-1753)Online publication date: 1-Oct-2019
https://dl.acm.org/doi/10.1007/s11063-018-9956-8
Avudai Selvi PRamanujam N(2017)A parameter uniform difference scheme for singularly perturbed parabolic delay differential equation with Robin type boundary conditionApplied Mathematics and Computation10.1016/j.amc.2016.10.027296:C(101-115)Online publication date: 1-Mar-2017
https://dl.acm.org/doi/10.1016/j.amc.2016.10.027

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