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A parameter-uniform numerical method for singularly perturbed Burgers’ equation

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Abstract

In this article, we propose a parameter-uniformly convergent numerical method for singularly perturbed Burgers’ initial-boundary value problem. First, the Burgers’ partial differential equation is semi-discretized in time using Crank–Nicolson finite difference method to yield a set of singularly perturbed nonlinear ordinary differential equations in space. The resulting two-point boundary value nonlinear singularly perturbed problems are linearized using Newton quasilinearization technique, and then, we apply fitted operator finite difference method to exhibit the layer nature of the solution. It is shown that the method converges uniformly with respect to the perturbation parameter. Numerical experiments are carried out to confirm the parameter-uniform nature of the scheme which is second-order convergent in time and first-order convergent in space.

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Acknowledgements

JB Munyakazi wishes to thank the National Research Foundation of South Africa. The authors are grateful for the reviewers’ constructive comments.

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Authors and Affiliations

  1. Department of Applied Mathematics, School of Applied Natural Sciences, Adama Science and Technology University, Po Box 1888,, Adama, Ethiopia

    Eshetu B. Derzie & Tekle Gemechu

  2. Department of Mathematics and Applied Mathematics, University of the Western Cape, Private BagX17, Bellville, 7535, South Africa

    Justin B. Munyakazi

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  1. Eshetu B. Derzie
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  2. Justin B. Munyakazi
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  3. Tekle Gemechu
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Correspondence to Justin B. Munyakazi.

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Derzie, E.B., Munyakazi, J.B. & Gemechu, T. A parameter-uniform numerical method for singularly perturbed Burgers’ equation. Comp. Appl. Math. 41, 247 (2022). https://doi.org/10.1007/s40314-022-01960-w

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  • DOI: https://doi.org/10.1007/s40314-022-01960-w

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