Numerical solution of nonlinear singular initial value problems of Emden–Fowler type using Chebyshev Neural Network method

Mall, Susmita; Chakraverty, Snehashish

doi:10.1016/j.neucom.2014.07.036

Cited by 80 publications

(32 citation statements)

References 40 publications

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“…In particular the formulations of ordinary differential equations (ODEs) are incorporated in detail with computation of the gradient of the network parameters with respect to its inputs [8,9].…”

Section: Formulation Of the Methodsmentioning

confidence: 99%

“…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%

“…The error computation involves both output and derivatives of the network output with respect to the corresponding inputs [8,9]. Then the gradient of network output with respect to their inputs for N(x, p)=z; sinh(z); tanh(z) is computed as below.…”

Section: Computation Of Gradient For Optimizing Values Of Weightmentioning

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%

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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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Section: Formulation Of the Methodsmentioning

confidence: 99%

“…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: Computation Of Gradient For Optimizing Values Of Weightmentioning

confidence: 99%

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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“…The Artificial neural network gave relief from repetition of iterative methods and interpolations. Also, one may use it as a black box to get numerical results at any arbitrary point in the domain [20]- [21].…”

Section: Introductionmentioning

confidence: 99%

A Neural Computational Intelligence Method Based on Legendre Polynomials for Fuzzy Fractional Order Differential Equation

Khan

Shaikh

Raja

et al. 2016

Journal of Applied Mathematics, Statistics and Informatics

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In this article, Legendre simulated annealing, neural network (LSANN) is designed for fuzzy fractional order differential equations, which is employed on fractional fuzzy initial value problem (FFIVP) with triangular condition. Here, Legendre polynomials are used to modify the structure of neural networks with a Taylor series approximation of the tangent hyperbolic as activation function while the network adaptive coefficients are trained in the procedure of simulated annealing to optimize the residual error. The computational results are depicted in terms of numerical values to compare them with previous results.

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