Design Collocation Neural Network for Solve regularly perturbed problems with Initial and Boundary conditions

Abstract

Recently, there has been an increasing interest in the study of regular and perturbed systems. The aim of this paper is to design artificial neural networks for solve regular perturbation problems with initial and boundary conditions. We design a multi-layer collocation neural 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.