Analysis of a nonlinear singularly perturbed Volterra integro-differential equation

Abstract

We consider a nonlinear singularly perturbed Volterra integro-differential equation. The problem is discretized by an implicit finite difference scheme on an arbitrary non-uniform mesh. The scheme comprises of an implicit difference operator for the derivative term and an appropriate quadrature rule for the integral term. We establish both a priori and a posteriori error estimates for the scheme that hold true uniformly in the small perturbation parameter. Numerical experiments are performed and results are reported for validation of the theoretical error estimates.