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International Conference on Finite Difference Methods

FDM 2018: Finite Difference Methods. Theory and Applications pp 484–492Cite as

A High Order Accurate Overlapping Domain Decomposition Method for Singularly Perturbed Reaction-Diffusion Systems

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11386))

Abstract

In this work, we consider a coupled system of singularly perturbed reaction-diffusion equations (SPRDEs) with distinct small positive parameters, exhibiting overlapping boundary layers at both ends of the domain. In [4], the authors designed an overlapping domain decomposition method that gives almost second order accurate approximations to the solution of coupled systems of SPRDEs. High order methods are of great significance to the numerical community. To this end, for numerically solving the coupled systems of SPRDEs, we designed a high order accurate overlapping domain decomposition method via. defining an appropriate decomposition of the original domain and then considering a hybrid difference scheme on a uniform mesh on each subdomain. More precisely, the method gives almost fourth order accurate approximations to the solution of the problem, as compared to almost second order accurate approximations in [4]. Numerical results are given to demonstrate the effectiveness of the proposed method.

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Authors and Affiliations

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

    Joginder Singh & Sunil Kumar

  2. Department of Mathematics, College of Charleston, Charleston, SC, USA

    Mukesh Kumar

Authors
  1. Joginder Singh
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  2. Sunil Kumar
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  3. Mukesh Kumar
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Corresponding author

Correspondence to Joginder Singh .

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Editors and Affiliations

  1. IICT, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Dimov

  2. Eötvös Loránd University, Budapest, Hungary

    István Faragó

  3. University of Rousse, Rousse, Bulgaria

    Lubin Vulkov

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Singh, J., Kumar, S., Kumar, M. (2019). A High Order Accurate Overlapping Domain Decomposition Method for Singularly Perturbed Reaction-Diffusion Systems. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Finite Difference Methods. Theory and Applications. FDM 2018. Lecture Notes in Computer Science(), vol 11386. Springer, Cham. https://doi.org/10.1007/978-3-030-11539-5_56

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  • DOI: https://doi.org/10.1007/978-3-030-11539-5_56

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-11538-8

  • Online ISBN: 978-3-030-11539-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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