Electron. J. Differential Equations, Vol. 2016 (2016), No. 331, pp. 1-18.

A new approach for solving nonlinear Thomas-Fermi equation based on fractional order of rational Bessel functions

Kourosh Parand, Amin Ghaderi, Hossein Yousefi, Mehdi Delkhosh

Abstract:
In this article, we introduce a fractional order of rational Bessel functions collocation method (FRBC) for solving the Thomas-Fermi equation. The problem is defined in the semi-infinite domain and has a singularity at x = 0 and its boundary condition occurs at infinity. We solve the problem on the semi-infinite domain without any domain truncation or transformation of the domain of the problem to a finite domain. This approach at first, obtains a sequence of linear differential equations by using the quasilinearization method (QLM), then at each iteration the equation is solves by FRBC method. To illustrate the reliability of this work, we compare the numerical results of the present method with some well-known results, to show that the new method is accurate, efficient and applicable.

Submitted June 16, 2016. Published December 27, 2016.
Math Subject Classifications: 34B16, 34B40, 74S25.
Key Words: Fractional order of rational Bessel functions; Collocation method; Thomas-Fermi equation; Quasilinearization method; Semi-infinite domain; Nonlinear ODE.

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Kourosh Parand
Department of Computer Sciences
Shahid Beheshti University, G.C.
Tehran, Iran
email: k_parand@sbu.ac.ir
Amin Ghaderi
Department of Computer Sciences
Shahid Beheshti University, G.C.
Tehran, Iran
email: amin.g.ghaderi@gmail.com
Hossein Yousefi
Department of Computer Sciences
Shahid Beheshti University, G.C.
Tehran, Iran
email: hyousefi412@gmail.com
Mehdi Delkhosh
Department of Computer Sciences
Shahid Beheshti University, G.C.
Tehran, Iran
email: mehdidelkhosh@yahoo.com

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