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An efficient numerical approximation for mixed singularly perturbed parabolic problems involving large time-lag

Author

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  • Sushree Priyadarshana

    (National Institute of Technology Rourkela)

  • Jugal Mohapatra

    (National Institute of Technology Rourkela)

Abstract

The objective of this work is to provide an efficient numerical scheme for solving singularly perturbed parabolic convection-diffusion problems with a large time lag having Robin-type boundary conditions. The implicit Euler scheme is used in the temporal direction on a uniform mesh. To handle the layer behavior caused due to the presence of perturbation parameter, the problem is solved using the upwind scheme on two layer-resolving meshes in the spatial direction. As the Shishkin mesh makes the order of convergence to one up to a logarithmic factor, in the spatial direction, the presence of this effect is prevented by the use of the Bakhvalov-Shishkin mesh. Further, the robustness of the scheme is tested over semi-linear time-lagged initial boundary value problems. Numerical outputs are presented in the form of tables and graphs to prove the parameter-uniform nature and robustness of the proposed scheme.

Suggested Citation

  • Sushree Priyadarshana & Jugal Mohapatra, 2024. "An efficient numerical approximation for mixed singularly perturbed parabolic problems involving large time-lag," Indian Journal of Pure and Applied Mathematics, Springer, vol. 55(4), pages 1389-1408, December.
    • Handle: RePEc:spr:indpam:v:55:y:2024:i:4:d:10.1007_s13226-023-00445-8
    DOI: 10.1007/s13226-023-00445-8
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    References listed on IDEAS

    as
    1. Gowrisankar, S. & Natesan, Srinivasan, 2019. "An efficient robust numerical method for singularly perturbed Burgers’ equation," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 385-394.
    2. Avudai Selvi, P. & Ramanujam, N., 2017. "A parameter uniform difference scheme for singularly perturbed parabolic delay differential equation with Robin type boundary condition," Applied Mathematics and Computation, Elsevier, vol. 296(C), pages 101-115.
    3. 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.
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