A fitted approximate method for a Volterra delay-integro-differential equation with initial layer

Abstract

This study is concerned with the finite-difference solution of singularly perturbed initial value problem for a linear first order Volterra integro-differential equation with delay. The method is based on the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with the weight and remainder terms in integral form. The emphasis is on the convergence of numerical method. It is shown that the method displays uniform convergence in respect to the perturbation parameter. Numerical results are also given.

Keywords

• Volterra delay-integro-differential equation,singular perturbation,finite difference,uniform convergence

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