Journal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Volume 17, Issue 11, Pages 4097-4103Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cnsns.2012.01.030
Keywords
Analytic solution; Thomas-Fermi equation; Homotopy analysis method; Computational cost; Pade approximant
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The explicit analytic solution of the Thomas-Fermi equation thorough a new kind of analytic technique, namely the homotopy analysis method, was employed by Liao [1]. However, the base functions and the auxiliary linear differential operator chosen were such that the convergence to the exact solution was fairly slow. New base functions and auxiliary linear operator to form a better homotopy are the main concern of the present paper. Optimum convergence control parameter concept is used together with a mathematical proof of the convergence. (C) 2012 Elsevier B.V. All rights reserved.
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