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.
Highlights
Perturbed delay differential equations play an important role in the modelling of several physical and biological phenomena like first exit time problems in modelling of activation of neuronal variability [3], bistable devices [8] and evolutionary biology [6] and in a variety of models for physiological processes or diseases [9],[10] and [11]
Parameter - uniform bounds for the error are given in the following theorem, which is the main result of this paper
The notations DN, pN, CpN, CpN∗ and p∗ bear the same meaning as in [2] but the methods to arrive at them are modified for the vector solution
Summary
Perturbed delay differential equations play an important role in the modelling of several physical and biological phenomena like first exit time problems in modelling of activation of neuronal variability [3], bistable devices [8] and evolutionary biology [6] and in a variety of models for physiological processes or diseases [9],[10] and [11]. An initial value problem for a system of semilinear delay differential equations is used to model tumor growth. Inequalities between vectors are understood in the componentwise sense
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