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A high order convergent adaptive numerical method for singularly perturbed nonlinear systems

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Abstract

In this work, we develop a high order convergent adaptive numerical method for a system of first-order singularly perturbed nonlinear differential equations with distinct perturbation parameters. The problem is discretized by a hybrid finite difference scheme for which a posteriori error estimate in the maximum norm is derived. The layer-adapted meshes are generated using equidistribution of the monitor function chosen based on the derived a posteriori error estimate. Numerical results are presented that validate the theory and show the effectiveness of the present numerical method.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, Uttar Pradesh, India

    Sumit, Shashikant Kumar & Sunil Kumar

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  1. Sumit
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  2. Shashikant Kumar
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  3. Sunil Kumar
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Correspondence to Sumit.

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Communicated by Jose Alberto Cuminato.

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Sumit, Kumar, S. & Kumar, S. A high order convergent adaptive numerical method for singularly perturbed nonlinear systems. Comp. Appl. Math. 41, 83 (2022). https://doi.org/10.1007/s40314-022-01788-4

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  • DOI: https://doi.org/10.1007/s40314-022-01788-4

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