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An Iterative Numerical Method for a Weakly Coupled System of Singularly Perturbed Convection–Diffusion Equations with Negative Shifts

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Abstract

In this paper, a numerical method based on an iterative scheme is proposed for a singularly perturbed weakly coupled system of delay differential equations of convection–diffusion type. 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. The numerical solutions of the non-delay problems are obtained by applying existing finite difference scheme for the non-delay weakly coupled system of singularly perturbed equations. An error estimate is derived by using maximum principle and in supremum norm. Numerical results illustrating the theory are also included.

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Authors and Affiliations

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

    P. Avudai Selvi & N. Ramanujam

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  1. P. Avudai Selvi
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  2. N. Ramanujam
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Correspondence to N. Ramanujam.

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Selvi, P.A., Ramanujam, N. An Iterative Numerical Method for a Weakly Coupled System of Singularly Perturbed Convection–Diffusion Equations with Negative Shifts. Int. J. Appl. Comput. Math 3 (Suppl 1), 147–160 (2017). https://doi.org/10.1007/s40819-017-0346-0

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  • DOI: https://doi.org/10.1007/s40819-017-0346-0

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