A Parameter Uniform Almost First Order Convergent Numerical Method for a Semi-Linear System of Singularly Perturbed Delay Differential Equations
Keywords:Perturbation problems, boundary layers, semi-linear delay differential equations, finite difference schemes, Shishkin mesh, parameter uniform convergence
AbstractIn 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.
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