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Journal
2014 | 12 | 7 | 503-510
Article title

Analytical approximate solutions to the Thomas-Fermi equation

Content
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Languages of publication
EN
Abstracts
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.
Publisher

Journal
Year
Volume
12
Issue
7
Pages
503-510
Physical description
Dates
published
1 - 7 - 2014
online
21 - 6 - 2014
Contributors
  • Department of Mathematics, Polytehnica University of Timişoara, Timişoara, 300006, Romania, remus.ene@upt.ro
References
  • [1] L. H. Thomas, Proc. Cambridge Philos. Soc. 23, 542 (1927) http://dx.doi.org/10.1017/S0305004100011683[Crossref]
  • [2] E. Fermi, Rend. Accad. del Lincei, Cl. Sci. Fis., Mat. e Nat. 6, 602 (1927)
  • [3] A. H. Nayfeh, D. T. Mook, Nonlinear Oscillations (John Wiley and Sond, New York, 1979)
  • [4] Yu Mitropolski, The Average Method in Nonlinear Mechanics (Naukova Dumka, Kiev, 1971)
  • [5] V. P. Agrwal, N. N. Denman, J. Sound Vib. 99, 463 (1985) http://dx.doi.org/10.1016/0022-460X(85)90534-6[Crossref]
  • [6] J. I. Ramos, J. Sound Vib. 307, 312 (2007) http://dx.doi.org/10.1016/j.jsv.2007.07.011[Crossref]
  • [7] A. M. Wazwaz, Mathematics and Computation 105, 11 (1999) http://dx.doi.org/10.1016/S0096-3003(98)10090-5[Crossref]
  • [8] A. Cedillo, J. Math. Phys. 34, 2713 (1993) http://dx.doi.org/10.1063/1.530090[Crossref]
  • [9] B. L. Burrows, P. W. Core, Quant. Appl. Math. 42, 73 (1984)
  • [10] M. Oulne, arxiv: physics/0511017v2 [physics atomph]
  • [11] C. M. Bender, K. A. Milton, S. S. Pinky, L. M. Simmons jr., J. Math. Phys. 30, 1447 (1989) http://dx.doi.org/10.1063/1.528326[Crossref]
  • [12] S. J. Liao, Beyond Perturbation. Introduction to the Homotopy Analysis Method (Chapman and Hall/CRC Press, Boca Raton, 2003) http://dx.doi.org/10.1201/9780203491164[Crossref]
  • [13] H. K. Khan, H. Xu, Phys. Lett. A 365, 111 (2007) http://dx.doi.org/10.1016/j.physleta.2006.12.064[Crossref]
  • [14] S. Esposito, Am. J. Phys. 70, 852 (2002) http://dx.doi.org/10.1119/1.1484144[Crossref]
  • [15] S. Esposito, Int. J. Theor. Phys. 41, 2417 (2002) http://dx.doi.org/10.1023/A:1021398203046[Crossref]
  • [16] E. Di Grezia, S. Esposito, Found. Phys., 1431 (2004)
  • [17] S. Kobayashi, et al., J. Phys. Soc. Japan 10, 759 (1955) http://dx.doi.org/10.1143/JPSJ.10.759[Crossref]
  • [18] V. Marinca, N. Herisanu, I. Nemes, Cent. Eur. J. Phys. 6, 648 (2008) http://dx.doi.org/10.2478/s11534-008-0061-x[Crossref]
  • [19] V. Marinca, N. Herisanu, C. Bota, B. Marinca, Applied Mathematics Letters 22, 245 (2009) http://dx.doi.org/10.1016/j.aml.2008.03.019[Crossref]
  • [20] V. Marinca, N. Herisanu, Mathematical Problems in Engineering, Article ID 169056 (2011) [WoS]
  • [21] V. Marinca, N. Herisanu, Nonlinear Dynamical Systems in Engineering - Some Approximate Approaches (Springer Verlag, Heidelberg, 2011) http://dx.doi.org/10.1007/978-3-642-22735-6[Crossref]
  • [22] R.-D. Ene, V. Marinca, R. Negrea, B. Caruntu, In: A. Voronkov et al. (Ed.), 14th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, Sep. 26–29, 2012, Timisoara, Romania (IEEE Computer Society, California 2012), 98
  • [23] V. Marinca, N. Herisanu, Scientific Research and Essays 8, 161 (2013)
  • [24] L. Elsgolts, Differential Equations and the Calculus of Variations (Mir Publishers, Moscow, 1980)
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.-psjd-doi-10_2478_s11534-014-0472-9
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