A New Stochastic Technique for Painlevé Equation-I Using Neural Network Optimized with Swarm Intelligence

A New Stochastic Technique for Painlevé Equation-I Using Neural Network Optimized with Swarm Intelligence

A methodology for solution of Painlevé equation-I is presented using computational intelligence technique based on neural networks and particle swarm optimization hybridized with active set algorithm. The mathematical model of the equation is developed with the help of linear combination of feed-for...

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Main Authors: Muhammad Asif Zahoor Raja, Junaid Ali Khan, Siraj-ul-Islam Ahmad, Ijaz Mansoor Qureshi
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Computational Intelligence and Neuroscience
Online Access:http://dx.doi.org/10.1155/2012/721867
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spelling doaj-8a678041cd644348b6b6d91e04794f7b2020-11-24T22:16:16ZengHindawi LimitedComputational Intelligence and Neuroscience1687-52651687-52732012-01-01201210.1155/2012/721867721867A New Stochastic Technique for Painlevé Equation-I Using Neural Network Optimized with Swarm IntelligenceMuhammad Asif Zahoor Raja0Junaid Ali Khan1Siraj-ul-Islam Ahmad2Ijaz Mansoor Qureshi3Department of Electronic Engineering, International Islamic University, Islamabad, PakistanDepartment of Electronic Engineering, International Islamic University, Islamabad, PakistanCenter for Computational Intelligence, P.O. Box 2300, Islamabad, PakistanDepartment of Electronic Engineering, International Islamic University, Islamabad, PakistanA methodology for solution of Painlevé equation-I is presented using computational intelligence technique based on neural networks and particle swarm optimization hybridized with active set algorithm. The mathematical model of the equation is developed with the help of linear combination of feed-forward artificial neural networks that define the unsupervised error of the model. This error is minimized subject to the availability of appropriate weights of the networks. The learning of the weights is carried out using particle swarm optimization algorithm used as a tool for viable global search method, hybridized with active set algorithm for rapid local convergence. The accuracy, convergence rate, and computational complexity of the scheme are analyzed based on large number of independents runs and their comprehensive statistical analysis. The comparative studies of the results obtained are made with MATHEMATICA solutions, as well as, with variational iteration method and homotopy perturbation method.http://dx.doi.org/10.1155/2012/721867
collection DOAJ
language English
format Article
sources DOAJ
author Muhammad Asif Zahoor Raja
Junaid Ali Khan
Siraj-ul-Islam Ahmad
Ijaz Mansoor Qureshi
spellingShingle Muhammad Asif Zahoor Raja
Junaid Ali Khan
Siraj-ul-Islam Ahmad
Ijaz Mansoor Qureshi
A New Stochastic Technique for Painlevé Equation-I Using Neural Network Optimized with Swarm Intelligence
Computational Intelligence and Neuroscience
author_facet Muhammad Asif Zahoor Raja
Junaid Ali Khan
Siraj-ul-Islam Ahmad
Ijaz Mansoor Qureshi
author_sort Muhammad Asif Zahoor Raja
title A New Stochastic Technique for Painlevé Equation-I Using Neural Network Optimized with Swarm Intelligence
title_short A New Stochastic Technique for Painlevé Equation-I Using Neural Network Optimized with Swarm Intelligence
title_full A New Stochastic Technique for Painlevé Equation-I Using Neural Network Optimized with Swarm Intelligence
title_fullStr A New Stochastic Technique for Painlevé Equation-I Using Neural Network Optimized with Swarm Intelligence
title_full_unstemmed A New Stochastic Technique for Painlevé Equation-I Using Neural Network Optimized with Swarm Intelligence
title_sort new stochastic technique for painlevé equation-i using neural network optimized with swarm intelligence
publisher Hindawi Limited
series Computational Intelligence and Neuroscience
issn 1687-5265
1687-5273
publishDate 2012-01-01
description A methodology for solution of Painlevé equation-I is presented using computational intelligence technique based on neural networks and particle swarm optimization hybridized with active set algorithm. The mathematical model of the equation is developed with the help of linear combination of feed-forward artificial neural networks that define the unsupervised error of the model. This error is minimized subject to the availability of appropriate weights of the networks. The learning of the weights is carried out using particle swarm optimization algorithm used as a tool for viable global search method, hybridized with active set algorithm for rapid local convergence. The accuracy, convergence rate, and computational complexity of the scheme are analyzed based on large number of independents runs and their comprehensive statistical analysis. The comparative studies of the results obtained are made with MATHEMATICA solutions, as well as, with variational iteration method and homotopy perturbation method.
url http://dx.doi.org/10.1155/2012/721867
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