Numerical solution of Lane-Emden equation using neural network

Jalab, Hamid A.; Ibrahim, Rabha W.; Murad, Shayma Adil; Melhum, Amera I.; Hadid, Samir

doi:10.1063/1.4757505

Cited by 6 publications

(5 citation statements)

References 25 publications

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“…Jalab et al [70] have shown a numerical method based on neural network, for solving the Lane-Emden equations singular initial value problems. The numerical solution has been given for integer case and non integer case.…”

Section: The Methods Have Been Proposed To Solve Lane-emden Type Equa...mentioning

confidence: 99%

The rational Chebyshev of second kind collocation method for solving a class of astrophysics problems

Parand

Khaleqi

2016

Eur. Phys. J. Plus

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The Lane-Emden equation has been used to model several phenomenas in theoretical physics, mathematical physics and astrophysics such as the theory of stellar structure. This study is an attempt to utilize the collocation method with the Rational Chebyshev of Second Kind function (RSC) to solve the Lane-Emden equation over the semi-infinit interval [0, +∞). According to well-known results and comparing with previous methods, it can be said that this method is efficient and applicable.

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Section: The Methods Have Been Proposed To Solve Lane-emden Type Equa...mentioning

confidence: 99%

The rational Chebyshev of second kind collocation method for solving a class of astrophysics problems

Parand

Khaleqi

2016

Eur. Phys. J. Plus

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“…Undoubtedly, the theory of existence holds a paramount position within the realm of fractional calculus. Researchers have also come up with many results on the solutions of existence and uniqueness to the initial and boundary value problems (BVPs) of FDEs in the sense of Riemann-Liouville and Caputo fractional derivatives, see ( [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]).…”

Section: Introductionmentioning

confidence: 99%

On the Existence and Ulam Stability of BVP within Kernel Fractional Time

Saber,

Imsatfia,

Boulares

et al. 2023

Fractal Fract

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This manuscript, we establish novel findings regarding the existence of solutions for second-order fractional differential equations employing Ψ-Caputo fractional derivatives. The application of Banach’s fixed-point theorem (BFPT) ensures the uniqueness of the solutions, while Schauder’s fixed-point theorem (SFPT) is instrumental in determining the existence of these solutions. Furthermore, we assess the stability of the proposed equation using the Ulam–Hyers stability criterion. To illustrate our results, we provide a concrete example showcasing their practical implications.

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“…In fact, the subject of numerical methods for solving fractional differential equations has gained prominence and has been discussed by several authors, including a series of papers [25][26][27][28][29][30][31] and references cited therein, which include some recent studies on the approximation method for differential equations of fractional order. El-Ajou et al [32] extended the application of the homotopy analysis method (HAM) to provide symbolic approximate solution for twopoint boundary value problems of fractional order.…”

Section: Introductionmentioning

confidence: 99%

Certain Analysis of Solution for the Nonlinear Two-Point Boundary Value Problem with Caputo Fractional Derivative

Murad

2022

Journal of Function Spaces

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In this paper, the existence and uniqueness of solutions for a nonlinear fractional differential equation with a two-point boundary condition in a Banach space are investigated by using the contraction mapping principle and the Brouwer fixed-point theorem with Bielecki norm. The iterative scheme of the numerical solution for the nonlinear two-point boundary value problem will be discussed and illustrated by solving some problems. The well-known Ulam-Hyers and Ulam-Hyers-Rassias stability theorems are employed to establish the stability of solutions to the boundary value problem. In the end, we provided a couple of examples to support our results.

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Numerical solution of Lane-Emden equation using neural network

Abstract: This paper presents a numerical method based on neural network, for solving the Lane-Emden equations singular initial value problems. The numerical solution is given for integer case and non integer case. The non integer case is taken in the sense of Riemann-Liouville operators.

Cited by 6 publications

References 25 publications

The rational Chebyshev of second kind collocation method for solving a class of astrophysics problems

The rational Chebyshev of second kind collocation method for solving a class of astrophysics problems

On the Existence and Ulam Stability of BVP within Kernel Fractional Time

Certain Analysis of Solution for the Nonlinear Two-Point Boundary Value Problem with Caputo Fractional Derivative

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