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A robust fitted operator finite difference method for singularly perturbed problems whose solution has an interior layer

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  • Munyakazi, Justin B.
  • Patidar, Kailash C.
  • Sayi, Mbani T.

Abstract

The objectives of this paper are to construct and study a fitted operator finite difference method for the class of singularly perturbed problems whose solution exhibits an interior layer due to the presence of a turning point. We first establish sharp bounds on the solution and its derivatives. Then in line with other fitted operator methods that are designed in various recent works in numerical singular perturbation theory by the first two authors, we propose a fitted operator finite difference method to solve this interior layer problem. This method is then analysed by making use of the bounds on the solutions that we derive. We show that the scheme is uniformly convergent of order one. We also apply Richardson extrapolation as the acceleration technique to improve the accuracy and the order of convergence of the scheme up to two. Numerical investigations are carried out to demonstrate the efficacy and robustness of the scheme.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:160:y:2019:i:c:p:155-167
    DOI: 10.1016/j.matcom.2018.12.010
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    Cited by:

    1. Kumar, Sunil & Sumit, & Vigo-Aguiar, Jesus, 2022. "A high order convergent numerical method for singularly perturbed time dependent problems using mesh equidistribution," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 199(C), pages 287-306.
    2. 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.
    3. Abraham J. Arenas & Gilberto González-Parra & Jhon J. Naranjo & Myladis Cogollo & Nicolás De La Espriella, 2021. "Mathematical Analysis and Numerical Solution of a Model of HIV with a Discrete Time Delay," Mathematics, MDPI, vol. 9(3), pages 1-21, January.
    4. Liu, Chein-Shan & Li, Botong, 2021. "Solving a singular beam equation by the method of energy boundary functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 419-435.

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