Series solution to the Thomas–Fermi equation

Abstract Here an analytic technique, namely the homotopy analysis method (HAM), is employed to solve the non-linear Thomas–Fermi equation. A new kind of transformation is being used here which has improved the results in comparison with Liao's work. We also present the comparison of this work with some well-known results and prove the importance of this transformation and the freedom of HAM.

[1]  S. Abbasbandy.  THE APPLICATION OF HOMOTOPY ANALYSIS METHOD TO NONLINEAR EQUATIONS ARISING IN HEAT TRANSFER , 2006 .

[2]  S. Liao.  A kind of approximate solution technique which does not depend upon small parameters — II. An application in fluid mechanics , 1997 .

[3]  L. H. Thomas.  The calculation of atomic fields , 1927, Mathematical Proceedings of the Cambridge Philosophical Society.

[4]  A. Cedillo.  A perturbative approach to the Thomas–Fermi equation in terms of the density , 1993 .

[5]  Shigehiro Kobayashi,et al.  Accurate Value of the Initial Slope of the Ordinary TF Function , 1955 .

[6]  T. Hayat,et al.  On analytic solution for thin film flow of a fourth grade fluid down a vertical cylinder , 2007 .

[7]  T. Hayat,et al.  Comparison between the HAM and HPM solutions of thin film flows of non-Newtonian fluids on a moving belt , 2007 .

[8]  Song‐Ping Zhu.  An exact and explicit solution for the valuation of American put options , 2006 .

[9]  E Hille.  On the Thomas-fermi equation. , 1969, Proceedings of the National Academy of Sciences of the United States of America.

[10]  T. Hayat,et al.  On the explicit analytic solutions of an Oldroyd 6-constant fluid , 2004 .

[11]  S. K. Pogrebnya,et al.  The analytical solution of the Thomas-Fermi equation for a neutral atom , 1987 .

[12]  G. Adomian.  Solution of the Thomas-Fermi equation , 1998 .

[13]  S. Liao,et al.  Beyond Perturbation: Introduction to the Homotopy Analysis Method , 2003 .

[14]  M. Ayub,et al.  Effects of partial slip on flow of a third grade fluid , 2006 .

[15]  S. Liao.  An approximate solution technique not depending on small parameters: A special example , 1995 .

[16]  T. Hayat,et al.  MHD boundary-layer flow of an upper-convected Maxwell fluid in a porous channel , 2006 .

[17]  Shijun Liao.  An explicit analytic solution to the Thomas-Fermi equation , 2003, Appl. Math. Comput..