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Computational and Experimental Investigation of Flow and Convective Heat Transfer Along Rough Surfaces Read chapter Read first chapter

2023 | OriginalPaper | Chapter

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

Authors : Sheetal Chawla, S. Chandra Sekhara Rao

Published in: Frontiers in Industrial and Applied Mathematics

Publisher: Springer Nature Singapore

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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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Metadata
Title
Numerical Treatment for a Coupled System of Singularly Perturbed Reaction–Diffusion Equations with Robin Boundary Conditions and Having Boundary and Interior Layers
Authors
Sheetal Chawla
S. Chandra Sekhara Rao
Copyright Year
2023
Publisher
Springer Nature Singapore
Book
Frontiers in Industrial and Applied Mathematics

Print ISBN: 978-981-19-7271-3

Electronic ISBN: 978-981-19-7272-0

Copyright Year: 2023

DOI
https://doi.org/10.1007/978-981-19-7272-0_44

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