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A fitted operator finite difference method of lines for singularly perturbed parabolic convection–diffusion problems

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  • Mbroh, Nana A.
  • Munyakazi, Justin B.

Abstract

We propose a uniformly convergent finite difference method to solve singularly perturbed time-dependent convection–diffusion problems in the framework of method of lines. The method uses the fitted operator finite difference method to discretize the spatial derivatives followed by the Crank–Nicolson method for the time derivative. Richardson extrapolation is performed in space to improve the accuracy of the method. We prove that the method is uniformly convergent with respect to the perturbation and the discretization parameters. We present numerical simulations to illustrate and confirm the theoretical results.

Suggested Citation

  • Mbroh, Nana A. & Munyakazi, Justin B., 2019. "A fitted operator finite difference method of lines for singularly perturbed parabolic convection–diffusion problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 165(C), pages 156-171.
    • Handle: RePEc:eee:matcom:v:165:y:2019:i:c:p:156-171
    DOI: 10.1016/j.matcom.2019.03.007
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    Cited by:

    1. Mbroh, Nana Adjoah & Noutchie, Suares Clovis Oukouomi & Massoukou, Rodrigue Yves M’pika, 2020. "A uniformly convergent finite difference scheme for Robin type singularly perturbed parabolic convection diffusion problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 174(C), pages 218-232.

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