An Explicit Analytic Solution to the Thomas-Fermi Equation by the Improved Differential Transform Method

H. Fatoorehchia and H. Abolghasemia,b aCenter for Separation Processes Modeling and Nano-Computations, School of Chemical Engineering, College of Engineering, University of Tehran, P.O. Box 11155/4563, Tehran, Iran bOil and Gas Center of Excellence, University of Tehran, Tehran, Iran

Received: March 29, 2013; Revised version: September 27, 2013; In final form: February 20, 2014

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In this paper, a newly proposed analytical scheme by the authors namely the improved differential transform method is employed to provide an explicit series solution to the Thomas-Fermi equation. The solution procedure is very straightforward, requiring merely elementary operations together with differentiation, and ends up in a recursive formula involving the Adomian polynomials to afford the unknown coefficients. Unlike many other methods, our approach is free of integration and hence can be of computational interest. In addition, a very good agreement between the proposed solution and the results from several well-known works in the literature is demonstrated.

DOI: 10.12693/APhysPolA.125.1083 PACS numbers: 02.30.Hq, 02.30.Mv, 02.60.Lj, 21.10.Ft, 31.15.-p