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An optimal iteration method with application to the Thomas-Fermi equation

100%

Marinca V. , Herişanu N.

Open Physics

2011

tom 9

nr 3

891-895

The aim of this paper is to introduce a new approximate method, namely the Optimal Parametric Iteration Method (OPIM) to provide an analytical approximate solution to Thomas-Fermi equation. This new iteration approach provides us with a convenient way to optimally control the convergence of the approximate solution. A good agreement between the obtained solution and some well-known results has been demonstrated. The proposed technique can be easily applied to handle other strongly nonlinear problems.

Analytical approximate solutions to the Thomas-Fermi equation

60%

Marinca V. , Ene R.-D.

Open Physics

2014

tom 12

nr 7

503-510

The purpose of this paper is to show how to use the Optimal Homotopy Asymptotic Method (OHAM) to solve the nonlinear differential Thomas-Fermi equation. Our procedure does not depend upon small parameters and provides us with a convenient way to optimally control the convergence of the approximate solutions. An excellent agreement was found between our approximate results and numerical solutions, which prove that OHAM is very efficient in practice, ensuring a very rapid convergence after only one iteration.