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

Authors: D. Shakti; J. Mohapatra

Addresses: Department of Mathematics, National Institute of Technology, Rourkela, 769008, India ' Department of Mathematics, National Institute of Technology, Rourkela, 769008, India

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.

Keywords: singular perturbation; upwind scheme; adaptive grid; integral boundary condition; boundary layer.

DOI: 10.1504/IJCSM.2019.102687

International Journal of Computing Science and Mathematics, 2019 Vol.10 No.4, pp.340 - 350

Received: 11 May 2017
Accepted: 19 Jul 2017

Published online: 01 Oct 2019 *

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