Application of Legendre Neural Network for solving ordinary differential equations

Abstract

In this paper, a new method based on single layer Legendre Neural Network (LeNN) model has been developed to solve initial and boundary value problems. In the proposed approach a Legendre polynomial based Functional Link Artificial Neural Network (FLANN) is developed. Nonlinear singular initial value problem (IVP), boundary value problem (BVP) and system of coupled ordinary differential equations are solved by the proposed approach to show the reliability of the method. The hidden layer is eliminated by expanding the input pattern using Legendre polynomials. Error back propagation algorithm is used for updating the network parameters (weights). Results obtained are compared with the existing methods and are found to be in good agreement.