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

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.