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An almost second order hybrid scheme for the numerical solution of singularly perturbed parabolic turning point problem with interior layer

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  • Yadav, Swati
  • Rai, Pratima

Abstract

In this article, we consider a one dimensional singularly perturbed parabolic convection–diffusion problem with interior turning point. The convection coefficient of the considered problem is vanishing inside the spatial domain and also, exhibits an interior layer. As a result, the exact solution of the considered problem contains an interior layer. A higher order numerical method is constructed and analyzed for the numerical solution of the considered problem. To discretize the time direction, we have used the classical implicit Euler method on a uniform mesh. Also, a hybrid finite difference scheme is employed on a generalized Shishkin mesh condensing in the interior layer region to discretize the spatial domain. Rigorous analysis is performed to show that the proposed method is ε-uniformly convergent of order almost two. The higher accuracy and convergence rate of the proposed scheme are verified via implementing numerical experiments on two test problems. Comparison is done with the scheme proposed in O’Riordan and Quinn (2015) for the considered class of problems.

Suggested Citation

  • Yadav, Swati & Rai, Pratima, 2021. "An almost second order hybrid scheme for the numerical solution of singularly perturbed parabolic turning point problem with interior layer," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 733-753.
    • Handle: RePEc:eee:matcom:v:185:y:2021:i:c:p:733-753
    DOI: 10.1016/j.matcom.2021.01.017
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    References listed on IDEAS

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    1. Yadav, Swati & Rai, Pratima, 2020. "A higher order numerical scheme for singularly perturbed parabolic turning point problems exhibiting twin boundary layers," Applied Mathematics and Computation, Elsevier, vol. 376(C).
    2. Munyakazi, Justin B. & Patidar, Kailash C. & Sayi, Mbani T., 2019. "A robust fitted operator finite difference method for singularly perturbed problems whose solution has an interior layer," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 160(C), pages 155-167.
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    Cited by:

    1. Sahoo, Sanjay Ku & Gupta, Vikas, 2023. "An almost second-order robust computational technique for singularly perturbed parabolic turning point problem with an interior layer," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 211(C), pages 192-213.

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