메뉴 건너뛰기




Volumn 218, Issue 14, 2012, Pages 7629-7637

Solution of Lane-Emden type equations using Legendre operational matrix of differentiation

Author keywords

Isothermal gas spheres equation; Lane Emden equations; Legendre operational matrix of differentiation

Indexed keywords

DIFFERENTIATION MATRICES; EFFICIENT NUMERICAL METHOD; ILLUSTRATIVE EXAMPLES; ISOTHERMAL GAS SPHERES EQUATION; LANE-EMDEN EQUATION; LANE-EMDEN TYPE EQUATIONS; LEGENDRE; LEGENDRE POLYNOMIALS; NUMERICAL TECHNIQUES; OPERATIONAL MATRIX OF DIFFERENTIATION;

EID: 84857454497     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2012.01.032     Document Type: Article
Times cited : (73)

References (27)
  • 2
    • 0348040939 scopus 로고
    • On theoretical temperature of the sun under the hypothesis of a gaseous mass maintaining its internal heat and depending on the laws of gases known to terrestrial experiment
    • J.H. Lane, On theoretical temperature of the sun under the hypothesis of a gaseous mass maintaining its internal heat and depending on the laws of gases known to terrestrial experiment, Am. J. Sci. Arts 2nd Series 50 (1870) 57-74.
    • (1870) Am. J. Sci. Arts 2nd Series , vol.50 , pp. 57-74
    • Lane, J.H.1
  • 4
    • 21144474137 scopus 로고
    • Nonperturbative approximate solution for Lane-Emden equation
    • N.T. Shawagfeh Nonperturbative approximate solution for Lane-Emden equation J. Math. Phys. 34 9 1993 4364 4369
    • (1993) J. Math. Phys. , vol.34 , Issue.9 , pp. 4364-4369
    • Shawagfeh, N.T.1
  • 5
    • 0040926145 scopus 로고    scopus 로고
    • A new algorithm for solving differential equation Lane-Emden type
    • A.M. Wazwaz A new algorithm for solving differential equation Lane-Emden type Appl. Math. Comput. 118 2001 287 310
    • (2001) Appl. Math. Comput. , vol.118 , pp. 287-310
    • Wazwaz, A.M.1
  • 6
    • 0035976505 scopus 로고    scopus 로고
    • Quasilinearization approach to nonlinear problems in physics with application to nonlinear ODEs
    • DOI 10.1016/S0010-4655(01)00415-5, PII S0010465501004155
    • V.B. Mandelzweig, and F. Tabakin Quasilinearization approach to nonlinear problems in physics with application to nonlinear ODEs Comput. Phys. Commun. 141 2001 268 281 (Pubitemid 33094166)
    • (2001) Computer Physics Communications , vol.141 , Issue.2 , pp. 268-281
    • Mandelzweig, V.B.1    Tabakin, F.2
  • 7
    • 0035879170 scopus 로고    scopus 로고
    • Numerical investigation of quasilinearization method in quantum mechanics
    • DOI 10.1016/S0010-4655(01)00191-6, PII S0010465501001916
    • R. Krivec, and V.B. Mandelzweig Numerical investigation of quasilinearization method in quantum mechanics Comput. Phys. Commun. 138 2001 69 79 (Pubitemid 32621488)
    • (2001) Computer Physics Communications , vol.138 , Issue.1 , pp. 69-79
    • Krivec, R.1    Mandelzweig, V.B.2
  • 8
    • 55549124176 scopus 로고    scopus 로고
    • Quasilinearization approach to computation with singular potentials
    • doi:10.1016/j.cpc.2008.07.006
    • R. Krivec, V.B. Mandelzweig, Quasilinearization approach to computation with singular potentials, Comput. Phys. Commun. doi:10.1016/j.cpc.2008.07.006.
    • Comput. Phys. Commun
    • Krivec, R.1    Mandelzweig, V.B.2
  • 9
    • 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 2003 199 208
    • (2003) Comput. Phys. Commun. , vol.153 , pp. 199-208
    • Ramos, J.I.1
  • 10
    • 0037542776 scopus 로고    scopus 로고
    • A new analytic algorithm of Lane-Emden type equations
    • S.J. Liao A new analytic algorithm of Lane-Emden type equations Appl. Math. Comput. 142 2003 1 16
    • (2003) Appl. Math. Comput. , vol.142 , pp. 1-16
    • Liao, S.J.1
  • 11
    • 0038182679 scopus 로고    scopus 로고
    • Variational approach to the Lane-Emden equation
    • J.H. He Variational approach to the Lane-Emden equation Appl. Math. Comput. 143 2003 539 541
    • (2003) Appl. Math. Comput. , vol.143 , pp. 539-541
    • He, J.H.1
  • 12
    • 0037844986 scopus 로고    scopus 로고
    • Variational approach to the six-order boundary value problems
    • J.H. He Variational approach to the six-order boundary value problems Appl. Math. Comput. 143 2003 537 538
    • (2003) Appl. Math. Comput. , vol.143 , pp. 537-538
    • He, J.H.1
  • 13
    • 0037844992 scopus 로고    scopus 로고
    • Variational approach to the Thomas-Fermi equation
    • J.H. He Variational approach to the Thomas-Fermi equation Appl. Math. Comput. 143 2003 533 535
    • (2003) Appl. Math. Comput. , vol.143 , pp. 533-535
    • He, J.H.1
  • 14
    • 0038182682 scopus 로고    scopus 로고
    • A Lagrangian for von Karman equations of large deflection problem of thin circular plate
    • J.H. He A Lagrangian for von Karman equations of large deflection problem of thin circular plate Appl. Math. Comput. 143 2003 543 549
    • (2003) Appl. Math. Comput. , vol.143 , pp. 543-549
    • He, J.H.1
  • 15
    • 67349166142 scopus 로고    scopus 로고
    • An analytic algorithm for Lane-Emden equations arising in Astrophysics using MHAM
    • O.P. Singh, R.K. Pandey, and V.K. Singh An analytic algorithm for Lane-Emden equations arising in Astrophysics using MHAM Comput. Phys. Commun. 180 2009 1116 1124
    • (2009) Comput. Phys. Commun. , vol.180 , pp. 1116-1124
    • Singh, O.P.1    Pandey, R.K.2    Singh, V.K.3
  • 16
    • 33750454785 scopus 로고    scopus 로고
    • Legendre wavelets method for solving differential equations of Lane-Emden type
    • DOI 10.1016/j.amc.2006.02.031, PII S0096300306002608
    • S.A. Yousefi Legendre wavelet method for solving differential equations of Lane-Emden type Appl. Math. Comput. 181 2006 1417 1422 (Pubitemid 44646613)
    • (2006) Applied Mathematics and Computation , vol.181 , Issue.2 , pp. 1417-1422
    • Yousefi, S.A.1
  • 17
    • 49549124481 scopus 로고    scopus 로고
    • Hybrid functions for nonlinear initial-value problems with applications to Lane-Emden type equations
    • H.R. Marzban, H.R. Tabrizidooz, and M. Razzaghi Hybrid functions for nonlinear initial-value problems with applications to Lane-Emden type equations Phys. Lett. A 372 2008 5883 5886
    • (2008) Phys. Lett. A , vol.372 , pp. 5883-5886
    • Marzban, H.R.1    Tabrizidooz, H.R.2    Razzaghi, M.3
  • 18
    • 34548509029 scopus 로고    scopus 로고
    • Approximate solution of a differential equation arising in astrophysics using the variational iteration method
    • DOI 10.1016/j.newast.2007.06.012, PII S1384107607000632
    • M. Dehghan, and F. Shakeri Approximate solution of a differential equation arising in astrophysics using variational iteration method New Astron. 13 2008 53 59 (Pubitemid 47371215)
    • (2008) New Astronomy , vol.13 , Issue.1 , pp. 53-59
    • Dehghan, M.1    Shakeri, F.2
  • 19
    • 70349807582 scopus 로고    scopus 로고
    • Rational Legendre pseudospectral approach for solving nonlinear differential equations of Lane-Emden type
    • K. Parand, M. Shahini, and M. Dehghan Rational Legendre pseudospectral approach for solving nonlinear differential equations of Lane-Emden 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
  • 20
    • 77950626787 scopus 로고    scopus 로고
    • An approximate algorithm for the solution of the nonlinear Lane-Emden type equations arising in astrophysics using Hermite function collocation method
    • K. Parand, M. Dehghan, A.R. Rezaei, and S.M. Ghaderi An approximate algorithm for the solution of the nonlinear Lane-Emden type equations arising in astrophysics using Hermite function collocation method Comput. Phys. Commun. 181 2010 1096 1108
    • (2010) Comput. Phys. Commun. , vol.181 , pp. 1096-1108
    • Parand, K.1    Dehghan, M.2    Rezaei, A.R.3    Ghaderi, S.M.4
  • 21
    • 77956404730 scopus 로고    scopus 로고
    • An elegant perturbation solution for the Lane-Emden equation of the second kind
    • R.A. Van Gorder An elegant perturbation solution for the Lane-Emden equation of the second kind New Astron. 16 2011 65 67
    • (2011) New Astron. , vol.16 , pp. 65-67
    • Van Gorder, R.A.1
  • 22
    • 79251626328 scopus 로고    scopus 로고
    • Analytical solutions to a quasilinear differential equation related to the Lane-Emden equation of the second kind
    • R.A. Van Gorder Analytical solutions to a quasilinear differential equation related to the Lane-Emden equation of the second kind Celestial Mech. Dynam. Astron. 109 2011 137 145
    • (2011) Celestial Mech. Dynam. Astron. , vol.109 , pp. 137-145
    • Van Gorder, R.A.1
  • 23
    • 79955837803 scopus 로고    scopus 로고
    • Application of optimal homotopy asymptotic method for the analytic solution of singular Lane-Emden type equation
    • S. Iqbal, and A. Javed Application of optimal homotopy asymptotic method for the analytic solution of singular Lane-Emden type equation Appl. Math. Comput. 217 2011 7753 7761
    • (2011) Appl. Math. Comput. , vol.217 , pp. 7753-7761
    • Iqbal, S.1    Javed, A.2
  • 24
    • 84857456526 scopus 로고    scopus 로고
    • An Approximation Algorithm for the solution of astrophysics equations using rational scaled generalized Laguerre function collocation method based on transformed Hermite-Gauss nodes
    • 10.4236/ijaa.2011.12010
    • A. Pirkhedri, P. Daneshjoo, H.H.S. Javadi, H. Navidi, S. Khodamoradi, and K. Ghaderi An Approximation Algorithm for the solution of astrophysics equations using rational scaled generalized Laguerre function collocation method based on transformed Hermite-Gauss nodes Int. J. Astron. Astrophys. 1 2011 67 72 10.4236/ijaa.2011.12010
    • (2011) Int. J. Astron. Astrophys. , vol.1 , pp. 67-72
    • Pirkhedri, A.1    Daneshjoo, P.2    Javadi, H.H.S.3    Navidi, H.4    Khodamoradi, S.5    Ghaderi, K.6
  • 25
    • 74249095517 scopus 로고    scopus 로고
    • A new operational matrix for solving fractional-order differential equations
    • A. Saadatmandi, and M. Dehghan A new operational matrix for solving fractional-order differential equations Comput. Math. Appl. 59 2010 1326 1336
    • (2010) Comput. Math. Appl. , vol.59 , pp. 1326-1336
    • Saadatmandi, A.1    Dehghan, M.2
  • 27
    • 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 2004 73 80
    • (2004) Int. J. Comput. Math. , vol.81 , pp. 73-80
    • Parand, K.1    Razzaghi, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.