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Volumn 67, Issue 7-8, 2010, Pages 673-680

Lagrangian method for solving LaneEmden type equation arising in astrophysics on semi-infinite domains

Author keywords

Astrophysics; Collocation method; Isothermal gas spheres; Lagrangian method; Laguerre functions; LaneEmden type equations; Nonlinear ODE

Indexed keywords

COLLOCATION METHOD; ISOTHERMAL GAS SPHERES; LAGRANGIAN METHODS; LAGUERRE FUNCTIONS; LANE-EMDEN TYPE EQUATIONS; NONLINEAR ODES;

EID: 78049432455     PISSN: 00945765     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.actaastro.2010.05.015     Document Type: Article
Times cited : (48)

References (45)
  • 1
    • 0034369460 scopus 로고    scopus 로고
    • LaguerreGalerkin method for nonlinear partial differential equations on a semi-infinite interval
    • B.Y. Guo, and J. Shen LaguerreGalerkin method for nonlinear partial differential equations on a semi-infinite interval Numer. Math. 86 4 2000 635 654
    • (2000) Numer. Math. , vol.86 , Issue.4 , pp. 635-654
    • Guo, B.Y.1    Shen, J.2
  • 2
    • 15044355275 scopus 로고    scopus 로고
    • Generalized Laguerre approximation and its applications to exterior problems
    • B.Y. Guo, J. Shen, and C.L. Xu Generalized Laguerre approximation and its applications to exterior problems J. Comp. Math. 23 2005 113 130
    • (2005) J. Comp. Math. , vol.23 , pp. 113-130
    • Guo, B.Y.1    Shen, J.2    Xu, C.L.3
  • 3
    • 0034432262 scopus 로고    scopus 로고
    • Stable and efficient spectral methods in unbounded domains using Laguerre functions
    • J. Shen Stable and efficient spectral methods in unbounded domains using Laguerre functions SIAM J. Numer. Anal. 38 4 2000 1113 1133
    • (2000) SIAM J. Numer. Anal. , vol.38 , Issue.4 , pp. 1113-1133
    • Shen, J.1
  • 4
    • 0345734982 scopus 로고    scopus 로고
    • Laguerre tau methods for solving higher order ordinary differential equations
    • H.I. Siyyam Laguerre tau methods for solving higher order ordinary differential equations J. Comput. Anal. Appl. 3 2 2001 173 182
    • (2001) J. Comput. Anal. Appl. , vol.3 , Issue.2 , pp. 173-182
    • Siyyam, H.I.1
  • 6
    • 0002665809 scopus 로고    scopus 로고
    • Jacobi spectral approximation and its applications to differential equations on the half line
    • B.Y. Guo Jacobi spectral approximation and its applications to differential equations on the half line J. Comput. Math. 18 1 2000 95 112
    • (2000) J. Comput. Math. , vol.18 , Issue.1 , pp. 95-112
    • Guo, B.Y.1
  • 8
    • 0002717130 scopus 로고
    • Orthogonal rational functions on a semi-infinite interval
    • J.P. Boyd Orthogonal rational functions on a semi-infinite interval J. Comput. Phys. 70 1 1987 63 88
    • (1987) J. Comput. Phys. , vol.70 , Issue.1 , pp. 63-88
    • Boyd, J.P.1
  • 9
    • 0034197003 scopus 로고    scopus 로고
    • A rational approximation and its applications to differential equations on the half line
    • B.Y. Guo, J. Shen, and Z.Q. Wang A rational approximation and its applications to differential equations on the half line J. Sci. Comput. 15 2 2000 117 147
    • (2000) J. Sci. Comput. , vol.15 , Issue.2 , pp. 117-147
    • Guo, B.Y.1    Shen, J.2    Wang, Z.Q.3
  • 10
    • 0038346445 scopus 로고    scopus 로고
    • Pseudospectral methods on a semi-infinite interval with application to the Hydrogen atom: A comparison of the mapped Fourier-sine method with Laguerre series and rational Chebyshev expansions
    • J.P. Boyd, C. Rangan, and P.H. Bucksbaum Pseudospectral methods on a semi-infinite interval with application to the Hydrogen atom: a comparison of the mapped Fourier-sine method with Laguerre series and rational Chebyshev expansions J. Comput. Phys. 188 1 2003 56 74
    • (2003) J. Comput. Phys. , vol.188 , Issue.1 , pp. 56-74
    • Boyd, J.P.1    Rangan, C.2    Bucksbaum, P.H.3
  • 11
    • 2442639373 scopus 로고    scopus 로고
    • Rational Legendre approximation for solving some physical problems on semi-infinite intervals
    • K. Parand, and M. Razzaghi Rational Legendre approximation for solving some physical problems on semi-infinite intervals Phys. Scr. 69 2004 353 357
    • (2004) Phys. Scr. , vol.69 , pp. 353-357
    • Parand, K.1    Razzaghi, M.2
  • 12
    • 57549098784 scopus 로고    scopus 로고
    • Rational Chebyshev tau method for solving higher-order ordinary differential equations
    • K. Parand, and M. Razzaghi Rational Chebyshev tau method for solving higher-order ordinary differential equations Int. J. Comput. Math. 81 1 2004 73 80
    • (2004) Int. J. Comput. Math. , vol.81 , Issue.1 , pp. 73-80
    • Parand, K.1    Razzaghi, M.2
  • 13
    • 0347758632 scopus 로고    scopus 로고
    • Rational Chebyshev tau method for solving Volterra's population model
    • K. Parand, and M. Razzaghi Rational Chebyshev tau method for solving Volterra's population model Appl. Math. Comput. 149 3 2004 893 900
    • (2004) Appl. Math. Comput. , vol.149 , Issue.3 , pp. 893-900
    • Parand, K.1    Razzaghi, M.2
  • 14
    • 70349807582 scopus 로고    scopus 로고
    • Rational Legendre pseudospectral approach for solving nonlinear differential equations of LaneEmden type
    • K. Parand, M. Shahini, and M. Dehghan Rational Legendre pseudospectral approach for solving nonlinear differential equations of LaneEmden type J. Comput. Phys. 228 2009 8830 8840
    • (2009) J. Comput. Phys. , vol.228 , pp. 8830-8840
    • Parand, K.1    Shahini, M.2    Dehghan, M.3
  • 16
    • 0141916942 scopus 로고
    • Cambridge University Press Cambridge
    • W. Thomson Collected Papers 1991 Cambridge University Press Cambridge
    • (1991) Collected Papers
    • Thomson, W.1
  • 17
    • 0003737969 scopus 로고
    • Teubner Leipzig and Berlin
    • R. Emden Gaskugeln 1907 Teubner Leipzig and Berlin
    • (1907) Gaskugeln
    • Emden, R.1
  • 20
    • 35349026707 scopus 로고    scopus 로고
    • Solution and asymptotic/blow-up behaviour of a class of nonlinear dissipative systems
    • G. Bluman, A.F. Cheviakov, and M. Senthilvelan Solution and asymptotic/blow-up behaviour of a class of nonlinear dissipative systems J. Math. Anal. Appl. 339 2008 1199 1209
    • (2008) J. Math. Anal. Appl. , vol.339 , pp. 1199-1209
    • Bluman, G.1    Cheviakov, A.F.2    Senthilvelan, M.3
  • 21
    • 0035535124 scopus 로고    scopus 로고
    • Symmetry transformations for the generalized Lane-Emden equation
    • DOI 10.1023/A:1010255807935
    • H. Goenner Symmetry transformations for the generalized LaneEmden equation Gen. Rel. Grav. 33 5 2001 833 841 (Pubitemid 33382587)
    • (2001) General Relativity and Gravitation , vol.33 , Issue.5 , pp. 833-841
    • Goenner, H.1
  • 22
    • 0034345397 scopus 로고    scopus 로고
    • Exact solutions of the generalized LaneEmden equation
    • H. Goenner, and P. Havas Exact solutions of the generalized LaneEmden equation J. Math. Phys. 41 2000 7029 7042
    • (2000) J. Math. Phys. , vol.41 , pp. 7029-7042
    • Goenner, H.1    Havas, P.2
  • 23
    • 0035976505 scopus 로고    scopus 로고
    • Quasilinearization approach to nonlinear problems in physics with application to nonlinear ODEs
    • V.B. Mandelzweig, and F. Tabakin Quasilinearization approach to nonlinear problems in physics with application to nonlinear ODEs Comput. Phys. Commun. 141 2 2001 268 281
    • (2001) Comput. Phys. Commun. , vol.141 , Issue.2 , pp. 268-281
    • Mandelzweig, V.B.1    Tabakin, F.2
  • 24
    • 21144474137 scopus 로고
    • Nonperturbative approximate solution for LaneEmden equation
    • N.T. Shawagfeh Nonperturbative approximate solution for LaneEmden equation J. Math. Phys. 34 9 1993 4364 4369
    • (1993) J. Math. Phys. , vol.34 , Issue.9 , pp. 4364-4369
    • Shawagfeh, N.T.1
  • 25
    • 0040926145 scopus 로고    scopus 로고
    • A new algorithm for solving differential equations of LaneEmden type
    • A. Wazwaz A new algorithm for solving differential equations of LaneEmden type Appl. Math. Comput. 118 23 2001 287 310
    • (2001) Appl. Math. Comput. , vol.118 , Issue.23 , pp. 287-310
    • Wazwaz, A.1
  • 26
    • 32144452761 scopus 로고    scopus 로고
    • The modified decomposition method for analytic treatment of differential equations
    • A. Wazwaz The modified decomposition method for analytic treatment of differential equations Appl. Math. Comput. 173 1 2006 165 176
    • (2006) Appl. Math. Comput. , vol.173 , Issue.1 , pp. 165-176
    • Wazwaz, A.1
  • 27
    • 0037542776 scopus 로고    scopus 로고
    • A new analytic algorithm of LaneEmden type equations
    • S. Liao A new analytic algorithm of LaneEmden type equations Appl. Math. Comput. 142 1 2003 1 16
    • (2003) Appl. Math. Comput. , vol.142 , Issue.1 , pp. 1-16
    • Liao, S.1
  • 28
    • 0038182679 scopus 로고    scopus 로고
    • Variational approach to the LaneEmden equation
    • J.H. He Variational approach to the LaneEmden equation Appl. Math. Comput. 143 23 2003 539 541
    • (2003) Appl. Math. Comput. , vol.143 , Issue.23 , pp. 539-541
    • He, J.H.1
  • 29
    • 10044270006 scopus 로고    scopus 로고
    • Linearization techniques for singular initial-value problems of ordinary differential equations
    • J.I. Ramos Linearization techniques for singular initial-value problems of ordinary differential equations Appl. Math. Comput. 161 2 2005 525 542
    • (2005) Appl. Math. Comput. , vol.161 , Issue.2 , pp. 525-542
    • Ramos, J.I.1
  • 30
    • 65149092716 scopus 로고    scopus 로고
    • Piecewise-adaptive decomposition methods
    • J.I. Ramos Piecewise-adaptive decomposition methods Chaos Solit. Fract. 40 4 2007 1623 1636
    • (2007) Chaos Solit. Fract. , vol.40 , Issue.4 , pp. 1623-1636
    • Ramos, J.I.1
  • 31
    • 43049098279 scopus 로고    scopus 로고
    • Series approach to the LaneEmden equation and comparison with the homotopy perturbation method
    • J.I. Ramos Series approach to the LaneEmden equation and comparison with the homotopy perturbation method Chaos Solit. Fract. 38 2 2008 400 408
    • (2008) Chaos Solit. Fract. , vol.38 , Issue.2 , pp. 400-408
    • Ramos, J.I.1
  • 32
    • 0037799370 scopus 로고    scopus 로고
    • Linearization methods in classical and quantum mechanics
    • J.I. Ramos Linearization methods in classical and quantum mechanics Comput. Phys. Commun. 153 2 2003 199 208
    • (2003) Comput. Phys. Commun. , vol.153 , Issue.2 , pp. 199-208
    • Ramos, J.I.1
  • 33
    • 33750454785 scopus 로고    scopus 로고
    • Legendre wavelets method for solving differential equations of LaneEmden type
    • S.A. Yousefi Legendre wavelets method for solving differential equations of LaneEmden type Appl. Math. Comput. 181 2 2006 1417 1422
    • (2006) Appl. Math. Comput. , vol.181 , Issue.2 , pp. 1417-1422
    • Yousefi, S.A.1
  • 34
    • 50349099602 scopus 로고    scopus 로고
    • Solutions of EmdenFowler equations by homotopy perturbation method
    • M.S.H. Chowdhury, and I. Hashim Solutions of EmdenFowler equations by homotopy perturbation method Nonlinear. Anal. Real World Appl. 10 2007 104 115
    • (2007) Nonlinear. Anal. Real World Appl. , vol.10 , pp. 104-115
    • Chowdhury, M.S.H.1    Hashim, I.2
  • 35
    • 43049103009 scopus 로고    scopus 로고
    • Determination of convergence intervals of the series solutions of EmdenFowler equations using polytropes and isothermal spheres
    • A. Aslanov Determination of convergence intervals of the series solutions of EmdenFowler equations using polytropes and isothermal spheres Phys. Lett. A 372 20 2008 3541 3740
    • (2008) Phys. Lett. A , vol.372 , Issue.20 , pp. 3541-3740
    • Aslanov, A.1
  • 36
    • 34548509029 scopus 로고    scopus 로고
    • Approximate solution of a differential equation arising in astrophysics using the variational iteration method
    • M. Dehghan, and F. Shakeri Approximate solution of a differential equation arising in astrophysics using the variational iteration method N. Astron. 13 1 2008 53 59
    • (2008) N. Astron. , vol.13 , Issue.1 , pp. 53-59
    • Dehghan, M.1    Shakeri, F.2
  • 37
    • 59049085436 scopus 로고    scopus 로고
    • Solutions of singular IVPs of LaneEmden type by the variational iteration method
    • A. Yildirim, and T. zi Solutions of singular IVPs of LaneEmden type by the variational iteration method Nonlinear Anal. Ser. A. Theory Method Appl. 70 6 2009 2480 2484
    • (2009) Nonlinear Anal. Ser. A. Theory Method Appl. , vol.70 , Issue.6 , pp. 2480-2484
    • Yildirim, A.1    Zi, T.2
  • 39
    • 49549124481 scopus 로고    scopus 로고
    • Hybrid functions for nonlinear initial-value problems with applications to LaneEmden type equations
    • H.R. Marzban, H.R. Tabrizidooz, and M. Razzaghi Hybrid functions for nonlinear initial-value problems with applications to LaneEmden type equations Phys. Lett. A 372 37 2008 5883 5886
    • (2008) Phys. Lett. A , vol.372 , Issue.37 , pp. 5883-5886
    • Marzban, H.R.1    Tabrizidooz, H.R.2    Razzaghi, M.3
  • 43
    • 0040836005 scopus 로고
    • Fractional integration for Laguerre expansions
    • G. Gasper, K. Stempak, and W. Trembels Fractional integration for Laguerre expansions Methods Appl. Anal. 2 1 1995 67 75
    • (1995) Methods Appl. Anal. , vol.2 , Issue.1 , pp. 67-75
    • Gasper, G.1    Stempak, K.2    Trembels, W.3
  • 44
    • 0002707624 scopus 로고
    • The optimization of convergence for Chebyshev polynomial methods in an unbounded domain
    • J.P. Boyd The optimization of convergence for Chebyshev polynomial methods in an unbounded domain J. Comput. Phys. 45 1982 43 79
    • (1982) J. Comput. Phys. , vol.45 , pp. 43-79
    • Boyd, J.P.1


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