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

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 diffi...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 247; pp. 100 - 114
Main Authors: Mall, Susmita, Chakraverty, S.
Format: Journal Article
Language:English
Published: Elsevier Inc 15.11.2014
Subjects:
Chebyshev approximation
Chebyshev Neural Network
Differential equations
Error back propagation algorithm
Feed forward neural network
Initial value problems
Lane–Emden equation
Learning theory
Mathematical analysis
Mathematical models
Neural networks
Non-linear second order ordinary differential equation
Polynomials
Lane–Emden equation
Chebyshev Neural Network
Non-linear second order ordinary differential equation
Feed forward neural network
Error back propagation algorithm
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary: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.
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ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2014.08.085