An analytic algorithm of Lane–Emden type equations arising in astrophysics using modified Homotopy analysis method

Singh, Om Prakash; Pandey, Rajesh K.; Singh, Vineet Kumar

doi:10.1016/j.cpc.2009.01.012

Cited by 94 publications

(67 citation statements)

References 31 publications

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“…We discussed the RKM and the GPS for solving the Lane-Emden equation with initial conditions expressed given by Equation (1). An example depicted in Equation (1) was presented and the computational accuracy was illustrated.…”

Section: Discussionmentioning

confidence: 99%

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Solving the Lane–Emden Equation within a Reproducing Kernel Method and Group Preserving Scheme

et al. 2017

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Section: Discussionmentioning

confidence: 99%

“…One of the equations in this class is the Lane-Emden equation [1]. We use the reproducing kernel method (RKM) and the group preserving scheme (GPS) to investigate this equation in this paper.…”

Section: Introductionmentioning

confidence: 99%

Solving the Lane–Emden Equation within a Reproducing Kernel Method and Group Preserving Scheme

et al. 2017

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“…Following non homogeneous Lane-Emden equations have been solved by Wazwaz [15] and Singh et al [13] using Adomian decomposition and modified homotopy analysis method. Here the same problem is solved using Chebyshev Neural Network.…”

Section: The Non Homogeneous Lane-emden Equationmentioning

confidence: 99%

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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“…(16)is the standart Lane-Emden equation that was used to model the thermal behavior of a spherical cloud of gas acting under the mutual attraction of its molecules and subject to the classical laws of thermodynamics and for g(x, y) = e y , h(x) = 0, Eq. (16) is the isothermal gas sphere equation, where the temperature remains constant[12][13][14][15][16][17][18][19][20].…”

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confidence: 99%

The Approximate Solution of High-Order Nonlinear Ordinary Differential Equations by Improved Collocation Method with Terms of Shifted Chebyshev Polynomials

Öztürk

Gülsu

2015

Int. J. Appl. Comput. Math

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In this paper, we present a direct computational method for solving the higher-order nonlinear differential equations by using collocation method. This method transforms the nonlinear differential equation into the system of nonlinear algebraic equations with unknown shifted Chebyshev coefficients, via Chebyshev-Gauss collocation points. The solution of this system yields the Chebyshev coefficients of the solution function. The method is valid for both initial-value and boundary-value problems. Several examples are presented to illustrate the accuracy and effectiveness of the method by the approximate solutions of very important equations of applied mathematics such as Lane-Emden equation, Riccati equation, Van der Pol equation. The approximate solutions can be very easily calculated using computer program Maple 13.

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An analytic algorithm of Lane–Emden type equations arising in astrophysics using modified Homotopy analysis method

Cited by 94 publications

References 31 publications

Solving the Lane–Emden Equation within a Reproducing Kernel Method and Group Preserving Scheme

Solving the Lane–Emden Equation within a Reproducing Kernel Method and Group Preserving Scheme

Chebyshev neural network model with linear and nonlinear active functions

The Approximate Solution of High-Order Nonlinear Ordinary Differential Equations by Improved Collocation Method with Terms of Shifted Chebyshev Polynomials

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