A uniformly convergent numerical scheme for singularly perturbed differential equation with integral boundary condition arising in neural network

Abstract

This article deals with a singularly perturbed quasilinear boundary value problem with integral boundary condition which arises in neural network. The problem is discretised by using an upwind finite difference scheme on a non-uniform mesh obtained via equidistribution of a monitor function. We prove that the method is first order convergent in the discrete maximum norm independent of perturbation parameter. The parameter uniform convergence is confirmed by numerical computations.