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A Numerical Method for a System of Singularly Perturbed Differential Equations of Reaction-Diffusion Type with Negative Shift

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Differential Equations and Numerical Analysis

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 172))

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Abstract

A numerical method based on an iterative scheme is proposed for a system of singularly perturbed differential equations of reaction-diffusion type with negative shift term. In this method the solution of the delay problem is obtained as the limit of the solutions to a sequence of the non-delay problems. Then non-delay problems are solved by applying available finite difference scheme and finite element method in the literature. An error estimate in supremum norm is derived. Numerical experiments are carried out.

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Acknowledgments

The first author thank the Department of Science and Technology, Government of India, for their financial support under the DST/INSPIRE Fellowship/2014/[IF140503].

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Authors and Affiliations

  1. Department of Mathematics, School of Mathematical Sciences, Bharathidasan University, Tiruchirappalli, 620024, Tamil Nadu, India

    P. Avudai Selvi & Ramanujam Narasimhan

Authors
  1. P. Avudai Selvi
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  2. Ramanujam Narasimhan
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Corresponding author

Correspondence to Ramanujam Narasimhan .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Bishop Heber College, Tiruchirappalli, Tamil Nadu, India

    Valarmathi Sigamani

  2. Institute for Numerical Computation and Analysis, Dublin, Ireland

    John J. H. Miller

  3. Department of Mathematics, Bharathidasan University, Tiruchirappalli, India

    Ramanujam Narasimhan

  4. Department of Mathematics, Bishop Heber College, Tiruchirappalli, India

    Paramasivam Mathiazhagan

  5. Department of Mathematics, Bishop Heber College, Tiruchirappalli, Tamil Nadu, India

    Franklin Victor

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Avudai Selvi, P., Narasimhan, R. (2016). A Numerical Method for a System of Singularly Perturbed Differential Equations of Reaction-Diffusion Type with Negative Shift. In: Sigamani, V., Miller, J., Narasimhan, R., Mathiazhagan, P., Victor, F. (eds) Differential Equations and Numerical Analysis. Springer Proceedings in Mathematics & Statistics, vol 172. Springer, New Delhi. https://doi.org/10.1007/978-81-322-3598-9_6

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