A robust numerical scheme for singularly perturbed delay parabolic initial-boundary-value problems involving mixed space shifts

Document Type : Research Paper

Authors

1 Department of Mathematics and Humanities, Kakatiya Institute of Technology and Science, Warangal, India.

2 Department of Mathematics, National Institute of Technology Rourkela, Odisha, India.

Abstract

This article proposes a parameter uniform numerical method for solving a singularly perturbed delay parabolic initial boundary-value problem involving mixed space shifts. The model also involves a large delay in time. Taylor’s series expansion is applied to approximate the retarded terms in the spatial direction. For the time discretization, the implicit trapezoidal scheme is applied on uniform mesh, and for the spatial discretization, we use a proper combination of the mid-point upwind and the central difference scheme on Shishkin mesh. The proposed scheme provides a second-order convergence rate uniformly with respect to the perturbation parameter. Some comparison results are presented by using the proposed method to support our claim.

Keywords

References

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Computational Methods for Differential Equations
Volume 11, Issue 1
January 2023
Pages 42-51

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History

  • Receive Date: 17 March 2022
  • Revise Date: 24 May 2022
  • Accept Date: 01 June 2022

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