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Volumn 217, Issue 12, 2011, Pages 5910-5922

Near-field and far-field approximations by the Adomian and asymptotic decomposition methods

Author keywords

Adomian decomposition method; Adomian polynomials; Asymptotic decomposition method; Nonlinear differential equations; Pad approximants; Solution continuation

Indexed keywords

ADOMIAN DECOMPOSITION METHOD; ADOMIAN POLYNOMIALS; APPROXIMANTS; ASYMPTOTIC DECOMPOSITION METHOD; NONLINEAR DIFFERENTIAL EQUATION;

EID: 79551627790     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2010.12.093     Document Type: Article
Times cited : (35)

References (30)
  • 2
    • 0020497451 scopus 로고
    • Inversion of nonlinear stochastic operators
    • G. Adomian, and R. Rach Inversion of nonlinear stochastic operators J. Math. Anal. Appl. 91 1983 39 46
    • (1983) J. Math. Anal. Appl. , vol.91 , pp. 39-46
    • Adomian, G.1    Rach, R.2
  • 6
    • 0021532132 scopus 로고
    • Light scattering in crystals
    • G. Adomian, and R. Rach Light scattering in crystals J. Appl. Phys. 56 1984 2592 2594
    • (1984) J. Appl. Phys. , vol.56 , pp. 2592-2594
    • Adomian, G.1    Rach, R.2
  • 8
    • 43049162263 scopus 로고
    • The decomposition method applied to stiff systems
    • G. Adomian, R. Rach, and M. Elrod The decomposition method applied to stiff systems Math. Comput. Simulat. 30 1988 271 276
    • (1988) Math. Comput. Simulat. , vol.30 , pp. 271-276
    • Adomian, G.1    Rach, R.2    Elrod, M.3
  • 9
    • 0008485419 scopus 로고
    • An efficient methodology for the physical sciences
    • G. Adomian, R. Rach, and R. Meyers An efficient methodology for the physical sciences Kybernetes 20 1991 24 34
    • (1991) Kybernetes , vol.20 , pp. 24-34
    • Adomian, G.1    Rach, R.2    Meyers, R.3
  • 10
    • 46749134732 scopus 로고    scopus 로고
    • Solving multi-term linear and non-linear diffusion-wave equations of fractional order by Adomian decomposition method
    • V. Daftardar-Gejji, and S. Bhalekar Solving multi-term linear and non-linear diffusion-wave equations of fractional order by Adomian decomposition method Appl. Math. Comput. 202 2008 113 120
    • (2008) Appl. Math. Comput. , vol.202 , pp. 113-120
    • Daftardar-Gejji, V.1    Bhalekar, S.2
  • 11
    • 41549107947 scopus 로고    scopus 로고
    • The decomposition method for solving the coupled modified KdV equations
    • A.A. Soliman, and M.A. Abdou The decomposition method for solving the coupled modified KdV equations Math. Comput. Model. 47 2008 1035 1041
    • (2008) Math. Comput. Model. , vol.47 , pp. 1035-1041
    • Soliman, A.A.1    Abdou, M.A.2
  • 12
    • 57649178470 scopus 로고    scopus 로고
    • Free vibration of non-uniform Euler-Bernoulli beams by the Adomian modified decomposition method
    • H.Y. Lai, C.K. Chen, and J.C. Hsu Free vibration of non-uniform Euler-Bernoulli beams by the Adomian modified decomposition method CMES - Comput. Model. Eng. Sci. 34 2008 87 116
    • (2008) CMES - Comput. Model. Eng. Sci. , vol.34 , pp. 87-116
    • Lai, H.Y.1    Chen, C.K.2    Hsu, J.C.3
  • 15
    • 0012945130 scopus 로고    scopus 로고
    • Numerical integration, analytic continuation, and decomposition
    • G. Adomian, R. Rach, and R. Meyers Numerical integration, analytic continuation, and decomposition Appl. Math. Comput. 88 1997 95 116
    • (1997) Appl. Math. Comput. , vol.88 , pp. 95-116
    • Adomian, G.1    Rach, R.2    Meyers, R.3
  • 16
    • 0002811385 scopus 로고    scopus 로고
    • Analytical approximations and Padé approximants for Volterra's population model
    • A.M. Wazwaz Analytical approximations and Padé approximants for Volterra's population model Appl. Math. Comput. 100 1999 13 25
    • (1999) Appl. Math. Comput. , vol.100 , pp. 13-25
    • Wazwaz, A.M.1
  • 17
    • 33751529463 scopus 로고    scopus 로고
    • Padé approximants and Adomian decomposition method for solving the Flierl-Petviashivili equation and its variants
    • A.M. Wazwaz Padé approximants and Adomian decomposition method for solving the Flierl-Petviashivili equation and its variants Appl. Math. Comput. 182 2006 1812 1818
    • (2006) Appl. Math. Comput. , vol.182 , pp. 1812-1818
    • Wazwaz, A.M.1
  • 18
    • 0036499003 scopus 로고    scopus 로고
    • An aftertreatment technique for improving the accuracy of Adomian's decomposition method
    • Y.C. Jiao, Y. Yamamoto, C. Dang, and Y. Hao An aftertreatment technique for improving the accuracy of Adomian's decomposition method Comput. Math. Appl. 43 2002 783 798
    • (2002) Comput. Math. Appl. , vol.43 , pp. 783-798
    • Jiao, Y.C.1    Yamamoto, Y.2    Dang, C.3    Hao, Y.4
  • 19
    • 0036376269 scopus 로고    scopus 로고
    • Improvement of convergence of Adomian's method using Padé approximants
    • M. Chrysos, F. Sanchez, and Y. Cherruault Improvement of convergence of Adomian's method using Padé approximants Kybernetes 31 2002 884 895
    • (2002) Kybernetes , vol.31 , pp. 884-895
    • Chrysos, M.1    Sanchez, F.2    Cherruault, Y.3
  • 20
    • 77949913663 scopus 로고    scopus 로고
    • Recurrence triangle for Adomian polynomials
    • J.S. Duan Recurrence triangle for Adomian polynomials Appl. Math. Comput. 216 2010 1235 1241
    • (2010) Appl. Math. Comput. , vol.216 , pp. 1235-1241
    • Duan, J.S.1
  • 21
    • 38249034598 scopus 로고
    • An investigation of the asymptotic decomposition method for nonlinear equations in physics
    • G. Adomian An investigation of the asymptotic decomposition method for nonlinear equations in physics Appl. Math. Comput. 24 1987 1 17
    • (1987) Appl. Math. Comput. , vol.24 , pp. 1-17
    • Adomian, G.1
  • 22
    • 0346397816 scopus 로고
    • An adaptation of the decomposition method for asymptotic solutions
    • G. Adomian An adaptation of the decomposition method for asymptotic solutions Math. Comput. Simulat. 30 1988 325 329
    • (1988) Math. Comput. Simulat. , vol.30 , pp. 325-329
    • Adomian, G.1
  • 23
    • 45549113881 scopus 로고
    • Solving the nonlinear equations of physics
    • G. Adomian Solving the nonlinear equations of physics Comput. Math. Appl. 16 1988 903 914
    • (1988) Comput. Math. Appl. , vol.16 , pp. 903-914
    • Adomian, G.1
  • 24
    • 0038875358 scopus 로고    scopus 로고
    • Integrations by asymptotic decomposition
    • K. Haldar, and B.K. Datta Integrations by asymptotic decomposition Appl. Math. Lett. 9 1996 81 83
    • (1996) Appl. Math. Lett. , vol.9 , pp. 81-83
    • Haldar, K.1    Datta, B.K.2
  • 25
    • 26444555975 scopus 로고    scopus 로고
    • Asymptotic decomposition method for solving mildly nonlinear differential equation
    • D.J. Evans, and K.A. Hossen Asymptotic decomposition method for solving mildly nonlinear differential equation Int. J. Comput. Math. 78 2001 569 573
    • (2001) Int. J. Comput. Math. , vol.78 , pp. 569-573
    • Evans, D.J.1    Hossen, K.A.2
  • 26
    • 0032391752 scopus 로고    scopus 로고
    • On the decomposition method to the heat equation with non-linear and non-local boundary conditions
    • M. Hadizadeh, and K. Maleknejad On the decomposition method to the heat equation with non-linear and non-local boundary conditions Kybernetes 27 1998 426 434
    • (1998) Kybernetes , vol.27 , pp. 426-434
    • Hadizadeh, M.1    Maleknejad, K.2
  • 27
    • 77958013614 scopus 로고    scopus 로고
    • An efficient algorithm for the multivariable Adomian polynomials
    • J.S. Duan An efficient algorithm for the multivariable Adomian polynomials Appl. Math. Comput. 217 2010 2456 2467
    • (2010) Appl. Math. Comput. , vol.217 , pp. 2456-2467
    • Duan, J.S.1
  • 28
    • 0021500393 scopus 로고
    • A convenient computational form for the Adomian polynomials
    • R. Rach A convenient computational form for the Adomian polynomials J. Math. Anal. Appl. 102 1984 415 419
    • (1984) J. Math. Anal. Appl. , vol.102 , pp. 415-419
    • Rach, R.1
  • 29
    • 0022101044 scopus 로고
    • Polynomial nonlinearities in differential equations
    • G. Adomian, and R. Rach Polynomial nonlinearities in differential equations J. Math. Anal. Appl. 109 1985 90 95
    • (1985) J. Math. Anal. Appl. , vol.109 , pp. 90-95
    • Adomian, G.1    Rach, R.2
  • 30
    • 0022675932 scopus 로고
    • SOLVING NONLINEAR DIFFERENTIAL EQUATIONS WITH DECIMAL POWER NONLINEARITIES
    • DOI 10.1016/0022-247X(86)90094-6
    • G. Adomian, and R. Rach Solving nonlinear differential equations with decimal power nonlinearities J. Math. Anal. Appl. 114 1986 423 425 (Pubitemid 16545712)
    • (1986) Journal of Mathematical Analysis and Applications , vol.114 , Issue.2 , pp. 423-425
    • Adomian, G.1    Rach, R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.