A New Approach for Numerical Solution of Singularly Perturbed Volterra Integro-Differential Equation

Abstract

This manuscript develops an efficient direct solver to investigateapproximate solution for singularly perturbed Volterra integro-differential equations (SPVIDE) of first order. Current approach dealswith the hybridization of finite difference technique followed by Simpson’s rule.Main characteristic behind this treatment is to convertsuch problem into lot simpler system of algebraic equations.To verify the applicability of the scheme numerical examples are encountered, whereas the numerical results depict the efficiency of proposed method. Apart from that, some theoretical study related to errorand boundedness of solution are also described to get a qualitative description of the scheme.