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Series solution to the Thomas-Fermi equation. (English) Zbl 1203.81060

Summary: 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.

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81V45 Atomic physics
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
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