Using collocation neural network to solve nonlinear singular differential equations

Abstract

The aim of this paper is to design collocation neural network to solve second order nonlinear boundary value problems in singular ordinary differential equations. The proposed network trained by back propagation with different training algorithms quasi-Newton, Levenberg–Marquardt, and Bayesian Regulation, were the designed network trained with those algorithms using the available experimental data as the training set and the proposed network containing a single hidden layer of five nodes. The next objective of this paper was to compare the performance of aforementioned algorithms with regard to predicting ability.