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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| Published in: | Applied mathematics and computation Vol. 247; pp. 100 - 114 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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15.11.2014
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| ISSN: | 0096-3003, 1873-5649 |
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| Abstract | 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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| AbstractList | 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. |
| Author | Chakraverty, S. Mall, Susmita |
| Author_xml | – sequence: 1 givenname: Susmita surname: Mall fullname: Mall, Susmita – sequence: 2 givenname: S. surname: Chakraverty fullname: Chakraverty, S. email: sne_chak@yahoo.com |
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| Keywords | Lane–Emden equation Chebyshev Neural Network Non-linear second order ordinary differential equation Feed forward neural network Error back propagation algorithm |
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| SubjectTerms | 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 |
| Title | Chebyshev Neural Network based model for solving Lane–Emden type equations |
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