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Uniformly convergent hybrid numerical scheme for singularly perturbed delay parabolic convection–diffusion problems on Shishkin mesh

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  • Das, Abhishek
  • Natesan, Srinivasan

Abstract

This article studies the numerical solution of singularly perturbed delay parabolic convection–diffusion initial-boundary-value problems. Since the solution of these problems exhibit regular boundary layers in the spatial variable, we use the piecewise-uniform Shishkin mesh for the discretization of the domain in the spatial direction, and uniform mesh in the temporal direction. The time derivative is discretized by the implicit-Euler scheme and the spatial derivatives are discretized by the hybrid scheme. For the proposed scheme, the stability analysis is carried out, and parameter-uniform error estimates are derived. Numerical examples are presented to show the accuracy and efficiency of the proposed scheme.

Suggested Citation

  • Das, Abhishek & Natesan, Srinivasan, 2015. "Uniformly convergent hybrid numerical scheme for singularly perturbed delay parabolic convection–diffusion problems on Shishkin mesh," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 168-186.
    • Handle: RePEc:eee:apmaco:v:271:y:2015:i:c:p:168-186
    DOI: 10.1016/j.amc.2015.08.137
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    Cited by:

    1. Yasir Nawaz & Muhammad Shoaib Arif & Wasfi Shatanawi & Amna Nazeer, 2021. "An Explicit Fourth-Order Compact Numerical Scheme for Heat Transfer of Boundary Layer Flow," Energies, MDPI, vol. 14(12), pages 1-17, June.
    2. Chen, Shu-Bo & Soradi-Zeid, Samaneh & Dutta, Hemen & Mesrizadeh, Mehdi & Jahanshahi, Hadi & Chu, Yu-Ming, 2021. "Reproducing kernel Hilbert space method for nonlinear second order singularly perturbed boundary value problems with time-delay," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    3. Priyadarshana, S. & Mohapatra, J. & Pattanaik, S.R., 2023. "An improved time accurate numerical estimation for singularly perturbed semilinear parabolic differential equations with small space shifts and a large time lag," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 214(C), pages 183-203.

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