Solving Nonlinear Lane-Emden Type Equations With Unsupervised

In this paper we propose a method for solving some well-known classes of lane-emden type equationswhich are nonlinear ordinary dierential equations on the semi-innite domain. the proposed approachis based on an unsupervised combined articial neural networks (ucann) method. firstly,the trial solutions of the dierential equations are written in the form of feed-forward neural networkscontaining adjustable parameters (the weights and biases); results are then optimized withthe combined neural network. the proposed method is tested on series of lane-emden dierentialequations and the results are reported. afterward, these results are compared with the solution ofother methods demonstrating the eciency and applicability of the proposed method.