Constructing two powerful methods to solve the Thomas-Fermi equation - Akgul, A.; Hashemi, M. S.; İnç, Mustafa; Raheem, S. A. (Springer, 2017)
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.
Keywords: SL(2, R)-shooting method; Group preserving scheme; Reproducing kernel method; Thomas-Fermi equation