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Numerical Treatment for a Coupled System of Singularly Perturbed Reaction–Diffusion Equations with Robin Boundary Conditions and Having Boundary and Interior Layers

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Frontiers in Industrial and Applied Mathematics (FIAM 2021)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 410))

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Abstract

A system of \(k(\ge 2)\) linear singularly perturbed differential equations of reaction–diffusion type coupled through their reactive terms is considered with Robin type boundary conditions, and the system has discontinuous source terms. The highest order derivative term of each equation is multiplied by a small positive parameter and these parameters are assumed to be different in magnitude, due to which the overlapping and interacting interior and boundary layers may appear in the solution of the considered problem. A numerical scheme involving a central difference scheme for the differential equations and a cubic spline technique for the Robin boundary conditions is developed on an appropriate piecewise-uniform Shishkin mesh. Error analysis is done and the constructed scheme is proved to be almost second-order uniformly convergent with respect to each perturbation parameter. Numerical experiments are conducted to verify the theoretical findings.

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Authors and Affiliations

  1. Department of Mathematics, Pt. N.R.S. Government College Rohtak, Haryana, 124001, India

    Sheetal Chawla

  2. Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, 110 016, India

    S. Chandra Sekhara Rao

Authors
  1. Sheetal Chawla
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  2. S. Chandra Sekhara Rao
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Correspondence to S. Chandra Sekhara Rao .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Institute of Technology, Nirma University, Ahmedabad, India

    Rajesh Kumar Sharma

  2. Dipartimento Di Matematica, University of Ferrara, Ferrara, Italy

    Lorenzo Pareschi

  3. Institute for Groundwater Studies, University of the Free State, Bloemfontein, South Africa

    Abdon Atangana

  4. Department of Mathematics, National Institute of Technology Rourkela, Rourkela, Odisha, India

    Bikash Sahoo

  5. Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal, India

    Vijay Kumar Kukreja

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Chawla, S., Rao, S.C.S. (2023). Numerical Treatment for a Coupled System of Singularly Perturbed Reaction–Diffusion Equations with Robin Boundary Conditions and Having Boundary and Interior Layers. In: Sharma, R.K., Pareschi, L., Atangana, A., Sahoo, B., Kukreja, V.K. (eds) Frontiers in Industrial and Applied Mathematics. FIAM 2021. Springer Proceedings in Mathematics & Statistics, vol 410. Springer, Singapore. https://doi.org/10.1007/978-981-19-7272-0_44

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