Using Neural Network To Solve Nonlinear Singular Perturbation Problems

Abstract

The aim of this paper is to solve nonlinear singular perturbation problems by using neural network. We use a multi-layer network having one hidden layer with 5 hidden units (neurons) and one linear output unit the sigmoid activation function of each hidden unit is ridge basis function where the network trained by back propagation with different training algorithms such as quasi-Newton, Levenberg-Marquardt, and Bayesian Regulation. Finally the results of numerical experiments are compared with the exact solution in illustrative examples to confirm the accuracy and efficiency of the presented scheme.