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A New Parameter-Uniform Discretization of Semilinear Singularly Perturbed Problems

Author

Listed:
  • Justin B. Munyakazi

    (Department of Mathematics and Applied Mathematics, University of the Western Cape, Private Bag X17, Bellville 7535, South Africa)

  • Olawale O. Kehinde

    (Department of Mathematics and Applied Mathematics, University of the Western Cape, Private Bag X17, Bellville 7535, South Africa)

Abstract

In this paper, we present a numerical approach to solving singularly perturbed semilinear convection-diffusion problems. The nonlinear part of the problem is linearized via the quasilinearization technique. We then design and implement a fitted operator finite difference method to solve the sequence of linear singularly perturbed problems that emerges from the quasilinearization process. We carry out a rigorous analysis to attest to the convergence of the proposed procedure and notice that the method is first-order uniformly convergent. Some numerical evaluations are implemented on model examples to confirm the proposed theoretical results and to show the efficiency of the method.

Suggested Citation

  • Justin B. Munyakazi & Olawale O. Kehinde, 2022. "A New Parameter-Uniform Discretization of Semilinear Singularly Perturbed Problems," Mathematics, MDPI, vol. 10(13), pages 1-14, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2254-:d:849210
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    References listed on IDEAS

    as
    1. Chandra Sekhara Rao, S. & Chaturvedi, Abhay Kumar, 2022. "Analysis of an almost fourth-order parameter-uniformly convergent numerical method for singularly perturbed semilinear reaction-diffusion system with non-smooth source term," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    2. Kabeto, Masho Jima & Duressa, Gemechis File, 2021. "Robust numerical method for singularly perturbed semilinear parabolic differential difference equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 537-547.
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    Cited by:

    1. Sergei Sitnik, 2023. "Editorial for the Special Issue “Analytical and Computational Methods in Differential Equations, Special Functions, Transmutations and Integral Transforms”," Mathematics, MDPI, vol. 11(15), pages 1-7, August.

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