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A series solution to the Thomas-Fermi equation. (English) Zbl 1161.34303

Summary: Nonlinear Thomas-Fermi equation is solved by an analytic technique named homotopy analysis method (HAM) in this paper. For a further improvement of the convergence and precision of the solution to Thomas-Fermi equation by HAM, different from previous work, however, a more generalized set of basis functions and consequential auxiliary linear operators are introduced to provide a series solution. Comparisons are also made between the results of the present work, some well-known numerical solution and previous work with the same technique, which shows the present work has provided a better series solution.

MSC:

34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
34A34 Nonlinear ordinary differential equations and systems
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