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

Mall, Susmita; Chakraverty, Snehashish

doi:10.1016/j.amc.2014.08.085

Cited by 84 publications

(55 citation statements)

References 33 publications

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“…Here n dimensional input pattern is expanded to m dimensional enhanced Chebyshev polynomials. Now, the weights of ChNN may be modified by using principle of back propagation [8,9],…”

Section: Learning Algorithm Of Chebyshev Neural Networkmentioning

confidence: 99%

“…A numerical method based on hybrid of Chebyshev wavelet and finite difference method has been proposed by Nasab et al [12] to solve the Lane-Emden equation which is reduce the computation of the problem to a set of nonlinear algebraic equations. In this paper, we are concerned for solving Lane-Emden type equations using Chebyshev neural network method with different active functions include a single layer and eliminated hidden layer by expanding the input pattern by Chebyshev polynomials [8,9]. To minimize the computed error function a feed forward neural network model with error back propagation principle is used.…”

Section: Introductionmentioning

confidence: 99%

“…The collocation method has been used by Mechee and Senu [10] to obtain the numerical solution of the Lane-Emden type. Recently, Chebyshev Neural Network based model has been used by Mall and Chakraverty [7] to solve the Lane-Emden type equations where the artificial neutral network used to solve the singularity in Lane-Emden type equations. A numerical method based on hybrid of Chebyshev wavelet and finite difference method has been proposed by Nasab et al [12] to solve the Lane-Emden equation which is reduce the computation of the problem to a set of nonlinear algebraic equations.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Chebyshev neural network model with linear and nonlinear active functions

Chaharborj

Mahmoudi²

2016

IJBAS

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In this paper the second order non-linear ordinary differential equations of Lane-Emden type as singular initial value problems using Chebyshev Neural Network (ChNN) with linear and nonlinear active functions has been studied. Active functions as, F(z)=z, sinh(x), tanh(z) are considered to find the numerical results with high accuracy. Numerical results from Chebyshev Neural Network shows that linear active function has more accuracy and is more convenient compare to other functions.

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“…Here n dimensional input pattern is expanded to m dimensional enhanced Chebyshev polynomials. Now, the weights of ChNN may be modified by using principle of back propagation [8,9],…”

Section: Learning Algorithm Of Chebyshev Neural Networkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Chebyshev neural network model with linear and nonlinear active functions

Chaharborj

Mahmoudi²

2016

IJBAS

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“…Also, Yousefi presented this study by Legendre scaling function [22,23]. To the best of our knowledge, the use of Bernstein polynomials to solve Emden-Fowler equations as singular initial value problems have not been considered in the literature, however, the Lane-Emden equation have been considered in [9,12,18,19] as initial value problems. It is noticed here that Bernstein polynomials have been used in some few restricted problems as singular differential equations, see [1, 6-8, 11, 13, 23].…”

Section: Introductionmentioning

confidence: 99%

Bernstein polynomials method for numerical solutions of integro-differential form of the singular Emden-Fowler initial value problems

Bencheikh¹,

Chiter²,

Abbassi³

2017

J. Math. Computer Sci.

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In this paper, Bernstein polynomial method applied to the solutions of generalized Emden-Fowler equations as singular initial value problems is presented. Firstly, the singular differential equations are converted to Volterra integro-differential equations and then solved by the Bernstein polynomials method. The properties of Bernstein polynomials via Gauss-Legendre rule are used to reduce the integral equations to a system of algebraic equations which can be solved numerically. Some illustrative examples are discussed to demonstrate the validity and applicability of the present method.

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“…-In 2014, Lane-Emden-Fowler equations were studied by Laguerre polynomial approach [11], Chebychev neural network (ChNN) [12] and by Differential transformation method (DTM) [13].…”

Section: Introductionmentioning

confidence: 99%

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

Khan

Shaikh

2017

Journal of Artificial Intelligence and Soft Computing Research

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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.

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

Cited by 84 publications

References 33 publications

Chebyshev neural network model with linear and nonlinear active functions

Chebyshev neural network model with linear and nonlinear active functions

Bernstein polynomials method for numerical solutions of integro-differential form of the singular Emden-Fowler initial value problems

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

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