A numerical approach for solving a class of the nonlinear Lane-Emden type equations arising in astrophysics

Yüzbaşı, Şuayip

doi:10.1002/mma.1519

Cited by 38 publications

(6 citation statements)

References 38 publications

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“…To utilize the Gauss pseudospectral tools, the domain OE0, l is first mapped to OE 1, C1 by using the affine transformation (12). Consequently, the following problem in OE 1, 1 is obtained:…”

Section: An Application Of the Proposed Methods For Finding The First mentioning

confidence: 99%

“…Dehghan and Shakeri [10] applied an exponential transformation to the Lane-Emden type equations to overcome the difficulty of a singular point at x D 0 and solved the resulting nonsingular problem by the variational iteration method. For other works placed to solve this class of nonlinear singular differential equations, see, for example, [6,[11][12][13][14][15][16][17][18][19][20].…”

Section: The Lane-emden-fowler Equationmentioning

confidence: 99%

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An efficient pseudospectral method for numerical solution of nonlinear singular initial and boundary value problems arising in astrophysics

Mehrpouya

2015

Math Methods in App Sciences

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In the manuscript, a pseudospectral method is developed for approximate and efficient solution of nonlinear singular Lane-Emden-Fowler initial and boundary value problems arising in astrophysics. In the proposed method, the Gauss pseudospectral method is utilized to reduce the problem to the solution of a system of algebraic equations. Furthermore, the Gauss pseudospectral method is developed for finding the first zero of the solution of this equation that gives the radius of the star, in which the numerous properties of the star such as mass, central pressure, and binding energy can be computed through their relations to this solution. The main advantage of the proposed method is that good results are obtained even by using a small number of discretization points and the rate of convergence is high. The accuracy and performance of the proposed method are examined by means of some numerical experiments.

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Section: An Application Of the Proposed Methods For Finding The First mentioning

confidence: 99%

Section: The Lane-emden-fowler Equationmentioning

confidence: 99%

An efficient pseudospectral method for numerical solution of nonlinear singular initial and boundary value problems arising in astrophysics

Mehrpouya

2015

Math Methods in App Sciences

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“…Briefly, the matrix forms for conditions are

{boldK}_{1} boldA = [α] or [{boldK}_{1}; α]

and

{boldK}_{2} boldA = [β] or [{boldK}_{2}; β],

where

K_{1} = X (0) D^{T} = [\begin{matrix} k_{1 0} & k_{1 1} & k_{1 2} & \dots & k_{1 N} \end{matrix}] and K_{2} = X (b) D^{T} = [\begin{matrix} k_{2 0} & k_{2 1} & k_{2 2} & \dots & k_{2 N} \end{matrix}] .

Consequently, to obtain the solution of Equation under conditions , by replacing the row matrices and by two rows of the matrix , we have the required augmented matrix

bold \tilde{W} boldA = bold \tilde{G} .

For simplicity, if last two rows of the matrix are replaced, the augmented matrix of the system is as follows :

([], bold \tilde{W}; bold \tilde{G}) = ([], \begin{matrix} w_{0 0} \end{matrix})

…”

Section: Collocation Methods Based On the Bessel Functions Of The Firsmentioning

confidence: 99%

“…Lately, Yüzbaşı et al . have solved the systems of Fredholm integro differential equations, the nonlinear Lane–Emden differential equations, complex differential equations, and systems of multi‐pantograph equations by means of the Bessel functions of the first kind.…”

Section: Introductionmentioning

confidence: 99%

A collocation method based on the Bessel functions of the first kind for singular perturbated differential equations and residual correction

Yüzbaşı

2014

Math Methods in App Sciences

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In this paper, a collocation method is given to solve singularly perturbated two-point boundary value problems. By using the collocation points, matrix operations and the matrix relations of the Bessel functions of the first kind and their derivatives, the boundary value problem is converted to a system of the matrix equations. By solving this system, the approximate solution is obtained. Also, an error problem is constructed by the residual function, and it is solved by the presented method. Thus, the error function is estimated, and the approximate solutions are improved. Finally, numerical examples are given to show the applicability of the method, and also, our results are compared by existing results.

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“…In this paper, by means of the matrix relations between the Bessel functions of first kind J n (x) and their derivatives, we apply the Bessel collocation method [19,20,21] to obtain approximate solutions of Hantavirus infection model studied in [12,13,14,22,23]. This model is characterized by a system of the nonlinear differential equations…”

Section: Introductionmentioning

confidence: 99%

Bessel collocation approach for approximate solutions of Hantavirus infection model

Yüzbaşı¹

2017

ntmsci

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Abstract:In this study, a collocation method is introduced to find the approximate solutions of Hantavirus infection model which is a system of nonlinear ordinary differential equations. The method is based on the Bessel functions of the first kind, matrix operations and collocation points. This method converts Hantavirus infection model into a matrix equation in terms of the Bessel functions of first kind, matrix operations and collocation points. The matrix equation corresponds to a system of nonlinear equations with the unknown Bessel coefficients. The reliability and efficiency of the suggested scheme are demonstrated by numerical applications and all numerical calculations have been done by using a program written in Maple.

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A numerical approach for solving a class of the nonlinear Lane-Emden type equations arising in astrophysics

Cited by 38 publications

References 38 publications

An efficient pseudospectral method for numerical solution of nonlinear singular initial and boundary value problems arising in astrophysics

An efficient pseudospectral method for numerical solution of nonlinear singular initial and boundary value problems arising in astrophysics

A collocation method based on the Bessel functions of the first kind for singular perturbated differential equations and residual correction

Bessel collocation approach for approximate solutions of Hantavirus infection model

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