A Parameter Uniform Almost First Order Convergent Numerical Method for a Semi-Linear System of Singularly Perturbed Delay Differential Equations

Authors

  • Nagaranjan Shivaranjan Bishop Heber College
  • John J H Miller Trinity College Dublin
  • Sigmani Valarmathi Bishop Heber College Tiruchirappalli

DOI:

https://doi.org/10.11145/j.biomath.2014.11.041

Keywords:

Perturbation problems, boundary layers, semi-linear delay differential equations, finite difference schemes, Shishkin mesh, parameter uniform convergence

Abstract

In this paper an initial value problem for asemi-linear 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.

Author Biographies

Nagaranjan Shivaranjan, Bishop Heber College

John J H Miller, Trinity College Dublin

Sigmani Valarmathi, Bishop Heber College Tiruchirappalli

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Published

2014-12-05

Issue

Vol. 3 No. 2 (2014)

Section

Original Articles

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