Solution of the Thomas-Fermi equation with a convergent approach


Turkyilmazoglu M.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, cilt.17, sa.11, ss.4097-4103, 2012 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 17 Konu: 11
  • Basım Tarihi: 2012
  • Doi Numarası: 10.1016/j.cnsns.2012.01.030
  • Dergi Adı: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
  • Sayfa Sayıları: ss.4097-4103

Özet

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.