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An Efficient Numerical Method for a System of Singularly Perturbed Semilinear Reaction-Diffusion Equations

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Book cover Numerical Methods and Applications (NMA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6046))

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Abstract

In this work we consider a system of singularly perturbed semilinear reaction-diffusion equations. To solve this problem numerically, we construct a finite difference scheme of Hermite type, and combine this with standard central difference scheme in a special way on a piecewise-uniform Shishkin mesh. We prove that the method is third order uniformly convergent. Numerical experiments are conducted to demonstrate the efficiency of the present method.

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Author information

Authors and Affiliations

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

    S. Chandra Sekhara Rao & Sunil Kumar

Authors
  1. S. Chandra Sekhara Rao
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  2. Sunil Kumar
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Editor information

Editors and Affiliations

  1. Institute of Computer and Communication Technologies, Bulgarian Academy of Sciences, Acad. G. Bonchev 25 A, 1113, Sofia, Bulgaria

    Ivan Dimov

  2. Faculty of Mathematics and Informatics, Department Numerical Methods and Algorithms, University of Sofia "St. Kliment Ohridski",, blvd. James Bourchier 5, 1164, Sofia, Bulgaria

    Stefka Dimova

  3. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. Bonchev St.,Bl.8, 1113, Sofia, Bulgaria

    Natalia Kolkovska

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Rao, S.C.S., Kumar, S. (2011). An Efficient Numerical Method for a System of Singularly Perturbed Semilinear Reaction-Diffusion Equations. In: Dimov, I., Dimova, S., Kolkovska, N. (eds) Numerical Methods and Applications. NMA 2010. Lecture Notes in Computer Science, vol 6046. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18466-6_58

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  • DOI: https://doi.org/10.1007/978-3-642-18466-6_58

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-18465-9

  • Online ISBN: 978-3-642-18466-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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