Nonlinear Dynamics

, Volume 87, Issue 2, pp 1435–1444 | Cite as

Constructing two powerful methods to solve the Thomas–Fermi equation

  • A. AkgülEmail author
  • M. S. Hashemi
  • M. Inc
  • S. A. Raheem
Original Paper


We implement the reproducing kernel method and SL(2, R)-shooting method to solve the Thomas–Fermi equation. Powerful techniques are demonstrated by reproducing kernel functions. The reliable numerical approximations to the solution of this equation are calculated by two novel approaches whose results are in good agreement. Numerical results are shown in order to prove the certainty of the techniques.


SL(2, R)-shooting method Group preserving scheme Reproducing kernel method Thomas–Fermi equation 



The authors would like to thank the referees for useful comments and remarks.


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of Mathematics, Art and Science FacultySiirt UniversitySiirtTurkey
  2. 2.Department of Mathematics, Basic Science FacultyUniversity of BonabBonabIran
  3. 3.Department of Mathematics, Science FacultyFirat UniversityElazigTurkey

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