A Robust Numerical Technique for Solving Non-Linear Volterra Integro-Differential Equations With Boundary Layer

Abstract

In this paper, we study a first-order non-linear singularly per-turbed Volterra integro-differential equation (SPVIDE). We discretize the problem by a uniform difference scheme on a Bakhvalov-Shishkin mesh. The scheme is constructed by the method of integral identities with expo-nential basis functions and integral terms are handled with interpolating quadrature rules with remainder terms. An effective quasi-linearization technique is employed for the algorithm. We establish the error estimates and demonstrate that the scheme on Bakhvalov-Shishkin mesh is O(N-1) uniformly convergent, where N is the mesh parameter. The numerical re-sults on a couple of examples are also provided to confirm the theoretical analysis.