Numerical solution of nonlinear singular initial value problems of Emden–Fowler type using Chebyshev Neural Network method

Abstract

In this investigation, a new algorithm has been proposed to solve singular initial value problems of Emden–Fowler type equations. Approximate solutions of these types of equations have been obtained by applying Chebyshev Neural Network (ChNN) model for the first time. The Emden–Fowler type equations are singular in nature. Here, we have considered single layer Chebyshev Neural Network model to overcome the difficulty of singularity. The computations become efficient because the procedure does not need to have hidden layer. A feed forward neural network model with error back propagation principle is used for modifying the network parameters and to minimize the computed error function. We have compared analytical and numerical solutions of linear and nonlinear Emden–Fowler equations respectively with the approximate solutions obtained by proposed ChNN method. Their good agreements and less CPU time in computations than the traditional artificial neural network (ANN) show the efficiency of the present methodology.