Parameter Uniform Numerical Methods for Singularly Perturbed Delay Differential Equation Involving Two Small Parameters

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This article deals with a singularly perturbed delay differential equation involving two small parameters. First, an upwind scheme is proposed on the fitted Shishkin mesh. The method is shown to be first order convergent. Then a hybrid scheme consisting of the midpoint upwind scheme in the outer region and the central difference scheme in the inner region is proposed. The error analysis is carried out for both the schemes and the accuracy is increased the from first order to second order. The performance of both schemes are assessed on some test problems and the results are in accord with the theoretical findings.