Fitted finite difference method for singularly perturbed delay differential equations

Authors:
Fevzi Erdogan;Gabil M. Amiraliyev
Affiliations:
Department of Mathematics, Faculty of Sciences, Yuzuncuyil University, Van, Turkey 65080;Department of Mathematics, Faculty of Sciences, Sinop University, Sinop, Turkey 57000
Venue:
Numerical Algorithms
Year:
2012

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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.