메뉴 건너뛰기




Volumn 218, Issue 17, 2012, Pages 8363-8369

The improved homotopy analysis method for the Thomas-Fermi equation

Author keywords

Homotopy analysis method; Nonlinear; Singularity; Thomas Fermi equation

Indexed keywords

HOMOTOPIES; HOMOTOPY ANALYSIS METHODS; INITIAL GUESS; LINEAR OPERATORS; NONLINEAR; RESIDUAL ERROR; SINGULARITY; THOMAS-FERMI EQUATION;

EID: 84862832762     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2012.02.004     Document Type: Article
Times cited : (38)

References (21)
  • 1
    • 84937022828 scopus 로고
    • The calculation of atomic fields
    • L. Thomas The calculation of atomic fields Proc. Cambridge Philos. Soc. 23 1927 542 548
    • (1927) Proc. Cambridge Philos. Soc. , vol.23 , pp. 542-548
    • Thomas, L.1
  • 2
    • 0038448396 scopus 로고
    • Thomas-Fermi equation solution by the differential analyzer
    • V. Bush, and S. Caldwell Thomas-Fermi equation solution by the differential analyzer Phys. Rev. 38 1931 1898 1902
    • (1931) Phys. Rev. , vol.38 , pp. 1898-1902
    • Bush, V.1    Caldwell, S.2
  • 3
    • 0038786022 scopus 로고
    • An analytic solution to the Thomas-Fermi equation
    • B. Laurenzi An analytic solution to the Thomas-Fermi equation J. Phys. A 31 1990 2535 2537
    • (1990) J. Phys. A , vol.31 , pp. 2535-2537
    • Laurenzi, B.1
  • 4
    • 21144468266 scopus 로고
    • A perturbative approach to the Thomas-Fermi equation in terms of the density
    • A. Cedillo A perturbative approach to the Thomas-Fermi equation in terms of the density J. Math. Phys. 34 1993 2713 2717
    • (1993) J. Math. Phys. , vol.34 , pp. 2713-2717
    • Cedillo, A.1
  • 5
    • 4243869886 scopus 로고
    • Modified variational solution of the Thomas-Fermi equation for atoms
    • M. Wu Modified variational solution of the Thomas-Fermi equation for atoms Phys. Rev. A 26 1982 57 61
    • (1982) Phys. Rev. A , vol.26 , pp. 57-61
    • Wu, M.1
  • 6
    • 0002751751 scopus 로고    scopus 로고
    • The modified decomposition method and pad approximants for solving the Thomas-Fermi equation
    • A. Wazwaz The modified decomposition method and pad approximants for solving the Thomas-Fermi equation Appl. Math. Comput. 105 1999 11 19
    • (1999) Appl. Math. Comput. , vol.105 , pp. 11-19
    • Wazwaz, A.1
  • 7
    • 57549102791 scopus 로고    scopus 로고
    • Rational Chebyshev pseudospectral approach for solving Thomas-Fermi equation
    • K. Parand, and M. Shahini Rational Chebyshev pseudospectral approach for solving Thomas-Fermi equation Phys. Lett. A 373 2009 210 213
    • (2009) Phys. Lett. A , vol.373 , pp. 210-213
    • Parand, K.1    Shahini, M.2
  • 8
    • 46749149602 scopus 로고    scopus 로고
    • Comment on: "Series solution to the Thomas-Fermi equation" [Phys. Lett. A 365 (2007) 111]
    • F. Fernandez Comment on: "series solution to the Thomas-Fermi equation" [Phys. Lett. A 365 (2007) 111] Phys. Lett. A 372 2008 5258 5260
    • (2008) Phys. Lett. A , vol.372 , pp. 5258-5260
    • Fernandez, F.1
  • 9
    • 79952006343 scopus 로고    scopus 로고
    • Rational approximation to the Thomas-Fermi equations
    • F. Fernandez Rational approximation to the Thomas-Fermi equations Appl. Math. Comput. 217 2011 6433 6436
    • (2011) Appl. Math. Comput. , vol.217 , pp. 6433-6436
    • Fernandez, F.1
  • 10
    • 77952464144 scopus 로고
    • Accurate value of the initial slope of the ordinary TF function
    • S. Kobayashi, S. Nagai, and K. Umeda Accurate value of the initial slope of the ordinary TF function J. Phys. Soc. Jpn. 10 1955 759 762
    • (1955) J. Phys. Soc. Jpn. , vol.10 , pp. 759-762
    • Kobayashi, S.1    Nagai, S.2    Umeda, K.3
  • 12
    • 0038451464 scopus 로고    scopus 로고
    • An explicit analytic solution to the Thomas-Fermi equation
    • S. Liao An explicit analytic solution to the Thomas-Fermi equation Appl. Math. Comput. 144 2003 495 506
    • (2003) Appl. Math. Comput. , vol.144 , pp. 495-506
    • Liao, S.1
  • 13
    • 34047186947 scopus 로고    scopus 로고
    • Series solution to the Thomas-Fermi equation
    • H. Khan, and H. Xu Series solution to the Thomas-Fermi equation Phys. Lett. A 365 2007 111 115
    • (2007) Phys. Lett. A , vol.365 , pp. 111-115
    • Khan, H.1    Xu, H.2
  • 14
    • 50249131883 scopus 로고    scopus 로고
    • A series solution to the Thomas-Fermi equation
    • B. Yao A series solution to the Thomas-Fermi equation Appl. Math. Comput. 203 2008 396 401
    • (2008) Appl. Math. Comput. , vol.203 , pp. 396-401
    • Yao, B.1
  • 15
    • 52949097284 scopus 로고    scopus 로고
    • Analytic approximations for Thomas-Fermi equation
    • A. El-Nahhas Analytic approximations for Thomas-Fermi equation Acta Phys. Pol., A. 114 2008 913 918
    • (2008) Acta Phys. Pol., A. , vol.114 , pp. 913-918
    • El-Nahhas, A.1
  • 16
    • 34548323392 scopus 로고
    • Equations of state of elements based on the generalized Fermi-Thomas theory
    • R. Feynman, N. Metropolis, and E. Teller Equations of state of elements based on the generalized Fermi-Thomas theory Phys. Rev. 75 1949 1561 1573
    • (1949) Phys. Rev. , vol.75 , pp. 1561-1573
    • Feynman, R.1    Metropolis, N.2    Teller, E.3
  • 17
    • 0002558447 scopus 로고
    • Momenta in atoms using the Thomas-Fermi method
    • C. Coulson, and N. March Momenta in atoms using the Thomas-Fermi method Proc. Phys. Soc. A 63 1950 367 374
    • (1950) Proc. Phys. Soc. A , vol.63 , pp. 367-374
    • Coulson, C.1    March, N.2
  • 18
    • 55549136027 scopus 로고    scopus 로고
    • Notes on the homotopy analysis method: Some definitions and theorems
    • S. Liao Notes on the homotopy analysis method: some definitions and theorems Commun. Nonlinear Sci. Numer. Simul. 14 2009 983 997
    • (2009) Commun. Nonlinear Sci. Numer. Simul. , vol.14 , pp. 983-997
    • Liao, S.1
  • 19
    • 76049117931 scopus 로고    scopus 로고
    • An optimal homotopy-analysis approach for strongly nonlinear differential equations
    • S. Liao An optimal homotopy-analysis approach for strongly nonlinear differential equations Commun. Nonlinear Sci. Numer. Simul. 15 2010 2003 2016
    • (2010) Commun. Nonlinear Sci. Numer. Simul. , vol.15 , pp. 2003-2016
    • Liao, S.1
  • 21
    • 0037300634 scopus 로고    scopus 로고
    • Homotopy analysis of nonlinear progressive waves in deep water
    • S. Liao, and K. Cheung Homotopy analysis of nonlinear progressive waves in deep water J. Eng. Math. 45 2003 105 116
    • (2003) J. Eng. Math. , vol.45 , pp. 105-116
    • Liao, S.1    Cheung, K.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.