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

100%
Marinca V., Herişanu N.
Open Physics
|
2011
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vol. 9
|
issue 3
891-895
EN
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.
2
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Analytical approximate solutions to the Thomas-Fermi equation

100%
Marinca V., Ene R.-D.
Open Physics
|
2014
|
vol. 12
|
issue 7
503-510
EN
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.
3
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Optimal homotopy asymptotic method with application to thin film flow

81%
Marinca V., Herişanu N., Nemeş I.
Open Physics
|
2008
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vol. 6
|
issue 3
648-653
EN
A new approximate analytical technique to address for non-linear problems, namely Optimal Homotopy Asymptotic Method (OHAM) is proposed and has been applied to thin film flow of a fourth grade fluid down a vertical cylinder. This approach however, does not depend upon any small/large parameters in comparison to other perturbation method. This method provides a convenient way to control the convergence of approximation series and allows adjustment of convergence regions where necessary. The series solution has been developed and the recurrence relations are given explicitly. The results reveal that the proposed method is very accurate, effective and easy to use.
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