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Abstract:Initial value problem for linear second order ordinary differential equation with small parameter by the first and second derivatives is considered. An exponentially fined difference scheme with constant fitting factors is developed in a uniform mesh, which gives first-order uniform convergence in the sense of discrete maximum norm. Numerical results are also presented.

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We consider the singularly perturbed initial value problem for a linear first order Volterra integro-differential equation with delay. Our purpose is to construct and analyse a numerical method with uniform convergence in the perturbation parameter. The numerical solution of this problem is discretised using an implicit difference rules for differential part and the composite numerical quadrature rules for integral part. On a layer-adapted mesh error estimations for the approximate solution are established. Numerical examples supporting the theory are presented.

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