Chebyshev Neural Network based model for solving Lane–Emden type equations

Abstract

The objective of this paper is to solve second order non-linear ordinary differential equations of Lane–Emden type using Chebyshev Neural Network (ChNN) model. These equations are categorized as singular initial value problems. Artificial Neural Network (ANN) model is used here to overcome the difficulty of the singularity. A single layer neural network is used and the hidden layer is eliminated by expanding the input pattern by Chebyshev polynomials. Here we have used feed forward neural network model and principle of error back propagation. Homogeneous and non-homogeneous Lane–Emden equations are considered to show effectiveness of Chebyshev Neural Network model.