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 problemswith initial and boundary conditions. We design a multi-layer collocation neural network havingone hidden layer with 5 hidden units (neurons) and one linear output unit the sigmoid activationfunction of each hidden unit is ridge basis function where the network trained by back propagationwith different training algorithms such as quasi-Newton, Levenberg-Marquardt, and BayesianRegulation. Finally the results of numerical experiments are compared with the exact solution inillustrative examples to confirm the accuracy and efficiency of the presented scheme.