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Fitted finite difference method for singularly perturbed delay differential equations

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Abstract

This paper deals with singularly perturbed initial value problem for linear second-order delay differential equation. An exponentially fitted difference scheme is constructed in an equidistant mesh, which gives first order uniform convergence in the discrete maximum norm. The difference scheme is shown to be uniformly convergent to the continuous solution with respect to the perturbation parameter. A numerical example is solved using the presented method and compared the computed result with exact solution of the problem.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, Yuzuncuyil University, 65080, Van, Turkey

    Fevzi Erdogan

  2. Department of Mathematics, Faculty of Sciences, Sinop University, 57000, Sinop, Turkey

    Gabil M. Amiraliyev

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  1. Fevzi Erdogan
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  2. Gabil M. Amiraliyev
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Correspondence to Fevzi Erdogan.

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Erdogan, F., Amiraliyev, G.M. Fitted finite difference method for singularly perturbed delay differential equations. Numer Algor 59, 131–145 (2012). https://doi.org/10.1007/s11075-011-9480-7

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  • DOI: https://doi.org/10.1007/s11075-011-9480-7

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