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

• Authors: Vasile Marinca , Nicolae Herişanu
• Languages of publication: EN

Abstracts

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.

Keywords

EN

Optimal Parametric Iteration Method (OPIM); Thomas-Fermi equation

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2011
• Volume: 9
• Issue: 3
• Pages: 891-895

Dates

published

1 - 6 - 2011

online

26 - 2 - 2011

Contributors

author

Vasile Marinca

• Politehnica University of Timişoara, Bd. M.Viteazu, nr. 1, 300222, Timişoara, Romania

author

Nicolae Herişanu

• Politehnica University of Timişoara, Bd. M.Viteazu, nr. 1, 300222, Timişoara, Romania

References

• [1] S. Kobayashi et al., J. Phys. Soc. Jpn. 10, 759 (1955) http://dx.doi.org/10.1143/JPSJ.10.759[Crossref]
• [2] B.L. Burrows, P.W. Core, Q. Appl. Math. 42, 73 (1984)
• [3] M.S. Wu, Phys. Rev. A 6, 57 (1982) http://dx.doi.org/10.1103/PhysRevA.26.57[Crossref]
• [4] J.H. He, H.M. Liu, Nonlinear Anal. Theory Methods Appl. 63, 919 (2005) http://dx.doi.org/10.1016/j.na.2005.01.086[Crossref]
• [5] H. Krutter, J. Comput. Phys. 47, 308 (1982) http://dx.doi.org/10.1016/0021-9991(82)90083-3[Crossref]
• [6] C. Grossmann, J. Comput. Phys. 98, 26 (1992) http://dx.doi.org/10.1016/0021-9991(92)90170-4[Crossref]
• [7] A. Cedillo, J. Math. Phys. 34, 2713 (1993) http://dx.doi.org/10.1063/1.530090[Crossref]
• [8] A.M. Wazwaz, Math. Comput. 105, 11 (1999)
• [9] S.J. Liao, Appl. Math. Comput. 144, 495 (2003) http://dx.doi.org/10.1016/S0096-3003(02)00423-X[Crossref]
• [10] S.J. Liao, Beyond perturbation: introduction to the homotopy analysis method (Chapmann & Hall/CRC Press, Boca Raton, 2003) http://dx.doi.org/10.1201/9780203491164[Crossref]
• [11] H. Khan, H. Xu, Phys. Lett. A 365, 111 (2009) http://dx.doi.org/10.1016/j.physleta.2006.12.064[Crossref]
• [12] B. Yao, Appl. Math. Comput. 203, 396 (2008) http://dx.doi.org/10.1016/j.amc.2008.04.050[Crossref]
• [13] C.Y. Chan, Y.C. Han, Q. Appl. Math. 45, 591 (1989)
• [14] J.I. Ramos, Comput. Phys. Commun. 158, 14 (2004) http://dx.doi.org/10.1016/j.comphy.2003.11.003[Crossref]
• [15] J.H. He, G.C. Wu, F. Austin, Nonlinear Science Letters A, 1, 1 (2010)
• [16] N. Herişanu, V. Marinca, Nonlinear Science Letters A, 1, 183 (2010)
• [17] R.E. Mickens, J. Sound Vib. 16, 185 (1987) http://dx.doi.org/10.1016/S0022-460X(87)81330-5[Crossref]
• [18] C.W. Lim, B.S. Wu, J. Sound Vib. 257, 202 (2002) http://dx.doi.org/10.1006/jsvi.2001.4233[Crossref]
• [19] V. Marinca, N. Herişanu, Acta Mech. 184, 231 (2006) http://dx.doi.org/10.1007/s00707-006-0336-5[Crossref]
• [20] N. Herişanu, V. Marinca, Int. J. Nonlin. Sci. Num. 10, 353 (2009) http://dx.doi.org/10.1515/IJNSNS.2009.10.3.353[Crossref]

Identifiers

DOI

10.2478/s11534-010-0059-z