Design Collocation Neural Network to Solve Singular Perturbation Problems for Partial Differential Equations

Abstract

he aim of this paper is to design neural network to present a method to solve Singular perturbation problems (SPP) for Partial Differential Equations (PDE’s) with initial and boundary conditions by using network having one hidden layer with 5 hidden units (neurons) and one linear output unit, the sigmoid activation of each hidden units is tansigmoid. The neural network trained by the back propagation with different 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.

Keywords: Singularly perturbed problems; Partial Differential Equations; Neural network; QuasiNewton; Levenberg-Marquardt, Bayesian  regulation.