A Machine Learning Model for Solving Lane-Emden Equation using Legendre Wavelet Neural Network

TL;DR

This paper introduces a Legendre wavelet neural network approach to solve the nonlinear Lane-Emden differential equation, demonstrating its effectiveness for singular initial value problems in engineering applications.

Contribution

The paper presents a novel LWNN method that efficiently handles singularities in Lane-Emden equations without hidden layers, using Legendre wavelets and error backpropagation.

Findings

Successfully solves second-order Lane-Emden equations

Validates the method's effectiveness for singular problems

Provides accurate solutions compared to traditional methods

Abstract

As we know differential equations are very useful for electrical engineers to solve a variety of problems like: voltage across a capacitor, input versus output voltage, etc. Therefore, the goal of this paper is to find the solutions of non-linear differential equations based on the Lane Emden equation of second order using the Legendre wavelet neural network (LWNN) method. Here all the considered equations are singular initial value problems. To manage the singularity challenge, we have employed an artificial neural network method. This approach utilizes a neural network of a single layer, where the hidden layer is omitted by enlarging the input using Legendre wavelets functions. We have applied a feed-forward neural network method to the proposed problem along with the principle of error backpropagation. The effectiveness of the Legendre wavelet Neural Network method is validated through Lane Emden equations..