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Fitted Difference Method For A Singularly Perturbed Initial Value Problem
Abstract
This study deals with the singularly perturbed initial value problem for a linear first order Volterra integro-differential equation with delay. First, asymptotic estimates for this problem are established which will be used for the analysis of the appropriate numerical solution. By the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with weight and remainder term in integral form, an exponential fitted difference scheme is constructed in a uniform mesh which gives first order uniform convergence in the discrete maximum norm. A numerical example is presented.
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