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A higher order numerical scheme for singularly perturbed parabolic turning point problems exhibiting twin boundary layers

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  • Yadav, Swati
  • Rai, Pratima

Abstract

In this article, a parameter-uniform numerical method is presented to solve one-dimensional singularly perturbed parabolic convection-diffusion multiple turning point problems exhibiting two exponential boundary layers. We study the asymptotic behaviour of the solution and its partial derivatives. The problem is discretized using the implicit Euler method for time discretization on a uniform mesh and a hybrid scheme for spatial discretization on a generalized Shishkin mesh. The scheme is shown to be ε-uniformly convergent of order one in time direction and order two in spatial direction upto a logarithmic factor. Numerical experiments are conducted to validate the theoretical results. Comparison is done with the upwind scheme on a uniform mesh as well as on the standard Shishkin mesh to demonstrate the higher order accuracy of the proposed scheme on a generalized Shishkin mesh.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:376:y:2020:i:c:s0096300320300643
    DOI: 10.1016/j.amc.2020.125095
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    Cited by:

    1. 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.
    2. Yadav, Swati & Rai, Pratima, 2023. "A parameter uniform higher order scheme for 2D singularly perturbed parabolic convection–diffusion problem with turning point," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 507-531.
    3. 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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