<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The actual motivation of this paper is to develop a functional link between artificial neural network (ANN) with Legendre polynomials and simulated annealing termed as Legendre simulated annealing neural network (LSANN). To demonstrate the applicability, it is employed to study the nonlinear Lane-Emden singular initial value problem that governs the polytropic and isothermal gas spheres. In LSANN, minimization of error is performed by simulated annealing method while Legendre polynomials are used in hidden layer to control the singularity problem. Many illustrative examples of Lane-Emden type are discussed and results are compared with the formerly used algorithms. As well as with accuracy of results and tranquil implementation it provides the numerical solution over the entire finite domain.</p></abstract>

The actual motivation of this paper is to develop a functional link between artificial neural network (ANN) with Legendre polynomials and simulated annealing termed as Legendre simulated annealing neural network (LSANN). To demonstrate the applicability, it is employed to study the nonlinear Lane-Emden singular initial value problem that governs the polytropic and isothermal gas spheres. In LSANN, minimization of error is performed by simulated annealing method while Legendre polynomials are used in hidden layer to control the singularity problem. Many illustrative examples of Lane-Emden type are discussed and results are compared with the formerly used algorithms. As well as with accuracy of results and tranquil implementation it provides the numerical solution over the entire finite domain.

A Smart Amalgamation of Spectral Neural Algorithm for Nonlinear Lane-Emden Equations with Simulated Annealing

Department of Mathematics, University of Karachi, Karachi 75270,

Journal of Artificial Intelligence and Soft Computing Research

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

The actual motivation of this paper is to develop a functional link between artificial neural network (ANN) with Legendre polynomials and simulated annealing...

A Smart Amalgamation of Spectral Neural Algorithm for Nonlinear Lane-Emden Equations with Simulated Annealing

Published Online: Mar 20, 2017

Page range: 215 - 224

Received: Jan 01, 2016

Accepted: Jul 04, 2016

DOI: https://doi.org/10.1515/jaiscr-2017-0015

Keywords
Lane-Emden equations, simulated annealing, legendre polynomials, neural network

© 2017 Academy of Management (SWSPiZ), Lodz

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

A Smart Amalgamation of Spectral Neural Algorithm for Nonlinear Lane-Emden Equations with Simulated Annealing

Published Online: Mar 20, 2017

Page range: 215 - 224

Received: Jan 01, 2016

Accepted: Jul 04, 2016

DOI: https://doi.org/10.1515/jaiscr-2017-0015

KeywordsLane-Emden equations, simulated annealing, legendre polynomials, neural network

© 2017 Academy of Management (SWSPiZ), Lodz

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Lane-Emden equations, simulated annealing, legendre polynomials, neural network