A Second-Order Upwind Difference Scheme for a Singularly Perturbed Problem with Integral Boundary Condition in Netural Network

Abstract

In this paper we consider a first order singularly perturbed quasilinear boundary value problem with integral boundary condition which arises in netural network. The problem is discretized using a hybrid upwind difference scheme on a Shishkin mesh. Applying the discrete maximum principle and barrier function techniques we show that the scheme is almost second order convergent, in the discrete maximum norm, independently of singular perturbation parameter. Numerical experiments support these theoretical results.KeywordsSingular perturbationupwind difference schemeShishkin meshuniform convergence