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A fourth-order numerical scheme for singularly perturbed delay parabolic problem arising in population dynamics

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Abstract

This article presents a higher-order parameter uniformly convergent method for a singularly perturbed delay parabolic reaction–diffusion initial-boundary-value problem. For the discretization of the time derivative, we use the implicit Euler scheme on the uniform mesh and for the spatial discretization, we use the central difference scheme on the Shishkin mesh, which provides a second-order convergence rate. To enhance the order of convergence, we apply the Richardson extrapolation technique. We prove that the proposed method converges uniformly with respect to the perturbation parameter and also attains almost fourth-order convergence rate. Finally, to support the theoretical results, we present some numerical experiments by using the proposed method.

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Acknowledgements

The authors express their thanks to unknown reviewers for valuable remarks and comments which improved the paper. The financial support received from SERB, Govt. of India via the research Grant No. EMR/2016/005805 is gratefully acknowledged.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Rourkela, Rourkela, 769008, India

    L. Govindarao & J. Mohapatra

  2. Faculty of Science and Technology, ICFAI University, Tripura Campus, Agartala, 799210, India

    A. Das

Authors
  1. L. Govindarao
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  2. J. Mohapatra
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  3. A. Das
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Correspondence to J. Mohapatra.

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Govindarao, L., Mohapatra, J. & Das, A. A fourth-order numerical scheme for singularly perturbed delay parabolic problem arising in population dynamics. J. Appl. Math. Comput. 63, 171–195 (2020). https://doi.org/10.1007/s12190-019-01313-7

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  • DOI: https://doi.org/10.1007/s12190-019-01313-7

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