A Parameter Uniform Method for an Initial Value Problem for a System of Singularly Perturbed Delay Differential Equations

Shivaranjani Nagarajan,J J H Miller,Valarmathi Sigamani,Ramanujam Narasimhan

doi:10.1007/978-3-319-06923-4_12

A Parameter Uniform Method for an Initial Value Problem for a System of Singularly Perturbed Delay Differential Equations

Shivaranjani Nagarajan, J J H Miller + Show 2 more

https://doi.org/10.1007/978-3-319-06923-4_12

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Publication Date: Jan 1, 2014

Citations: 2

Affiliation: Bharathidasan University

#Initial Value Problem For System #Interior Layers + Show 8 more

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Abstract

In this paper an initial value problem for a coupled system of two singularly perturbed first-order delay differential equations is considered on the interval (0,2]. The components of the solution of this system exhibit initial layers at 0 and interior layers at 1. A numerical method composed of a classical finite difference scheme on a piecewise uniform Shishkin mesh is suggested. This method is proved to be first-order convergent in the maximum norm uniformly in the perturbation parameters. A numerical illustration is provided to support the theory.

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