메뉴 건너뛰기




Volumn 62, Issue 5, 2011, Pages 2289-2303

A numerical approach for solving the high-order linear singular differential-difference equations

Author keywords

Approximate solutions; Collocation method; Collocation points; Singular differential difference equations; The Bessel matrix method; The Bessel polynomials and series

Indexed keywords

APPROXIMATE SOLUTION; BESSEL POLYNOMIALS; COLLOCATION METHOD; COLLOCATION POINTS; DIFFERENTIAL-DIFFERENCE EQUATIONS; MATRIX METHODS;

EID: 80052259398     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2011.07.016     Document Type: Article
Times cited : (36)

References (32)
  • 3
    • 3142537247 scopus 로고    scopus 로고
    • Higher order finite difference method for a class of singular boundary value problems
    • A.S.V. Ravi Kanth, and Y.N. Reddy Higher order finite difference method for a class of singular boundary value problems Appl. Math. Comput. 155 2004 249 258
    • (2004) Appl. Math. Comput. , vol.155 , pp. 249-258
    • Ravi Kanth, A.S.V.1    Reddy, Y.N.2
  • 4
    • 34247876015 scopus 로고    scopus 로고
    • An algorithm for solving singular perturbation problems with mechanization
    • DOI 10.1016/j.amc.2006.09.132, PII S009630030601352X
    • H.M. Habib, and E.R. El-Zahar An algorithm for solving singular perturbation problems with mechanization Appl. Math. Comput. 188 2007 286 302 (Pubitemid 46691324)
    • (2007) Applied Mathematics and Computation , vol.188 , Issue.1 , pp. 286-302
    • Habib, H.M.1    El-Zahar, E.R.2
  • 5
    • 0036682306 scopus 로고    scopus 로고
    • A three-point finite difference method for a class of singular two-point boundary value problems
    • DOI 10.1016/S0377-0427(01)00537-4, PII S0377042701005374
    • M. Kumar A three-point finite difference method for a class of singular two-point boundary value problems J. Comput. Appl. Math. 145 2002 89 97 (Pubitemid 34834420)
    • (2002) Journal of Computational and Applied Mathematics , vol.145 , Issue.1 , pp. 89-97
    • Kumar, M.1
  • 6
    • 0040926145 scopus 로고    scopus 로고
    • A new algorithm for solving differential equations of LaneEmden type
    • A.M. Wazwaz A new algorithm for solving differential equations of LaneEmden type Appl. Math. Comput. 118 2001 287 310
    • (2001) Appl. Math. Comput. , vol.118 , pp. 287-310
    • Wazwaz, A.M.1
  • 7
    • 58749094806 scopus 로고    scopus 로고
    • Solving singular boundary value problems of higher-order ordinary differential equations by modified Adomian decomposition method
    • Y.Q. Hasan, and L.M. Zhu Solving singular boundary value problems of higher-order ordinary differential equations by modified Adomian decomposition method Commun. Nonlinear Sci. Numer. Simul. 14 2009 2592 2596
    • (2009) Commun. Nonlinear Sci. Numer. Simul. , vol.14 , pp. 2592-2596
    • Hasan, Y.Q.1    Zhu, L.M.2
  • 8
    • 77956873280 scopus 로고    scopus 로고
    • Modified Adomian decomposition method and computer implementation for solving singular boundary value problems arising in various physical problems
    • M. Kumar, and N. Singh Modified Adomian decomposition method and computer implementation for solving singular boundary value problems arising in various physical problems Comput. Chem. Eng. 34 2010 1750 1760
    • (2010) Comput. Chem. Eng. , vol.34 , pp. 1750-1760
    • Kumar, M.1    Singh, N.2
  • 9
    • 77957922712 scopus 로고    scopus 로고
    • On using a modified Legendre-spectral method for solving singular IVPs of LaneEmden type
    • H. Adibi, and A.M. Rismani On using a modified Legendre-spectral method for solving singular IVPs of LaneEmden type Comput. Math. Appl. 60 2010 2126 2130
    • (2010) Comput. Math. Appl. , vol.60 , pp. 2126-2130
    • Adibi, H.1    Rismani, A.M.2
  • 10
    • 34548249064 scopus 로고    scopus 로고
    • Solutions of singular IVPs of LaneEmden type by homotopy perturbation method
    • A. Yildirim, and T. zi Solutions of singular IVPs of LaneEmden type by homotopy perturbation method Phys. Lett. A 369 2007 70 76
    • (2007) Phys. Lett. A , vol.369 , pp. 70-76
    • Yildirim, A.1    Zi, T.2
  • 11
    • 43049098279 scopus 로고    scopus 로고
    • Series approach to the Lane-Emden equation and comparison with the homotopy perturbation method
    • DOI 10.1016/j.chaos.2006.11.018, PII S0960077906010575
    • J.I. Ramos Series approach to the LaneEmden equation and comparison with the homotopy perturbation method Chaos Solitons Fractals 38 2008 400 408 (Pubitemid 351627012)
    • (2008) Chaos, Solitons and Fractals , vol.38 , Issue.2 , pp. 400-408
    • Ramos, J.I.1
  • 12
    • 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. RWA 10 2009 104 115
    • (2009) Nonlinear Anal. RWA , vol.10 , pp. 104-115
    • Chowdhury, M.S.H.1    Hashim, I.2
  • 13
    • 77957984152 scopus 로고    scopus 로고
    • A new method for solving a class of mixed boundary value problems with singular coefficient
    • Y.L. Wang, Z.Y. Li, Y. Cao, and X.H. Wan A new method for solving a class of mixed boundary value problems with singular coefficient Appl. Math. Comput. 217 2010 2768 2772
    • (2010) Appl. Math. Comput. , vol.217 , pp. 2768-2772
    • Wang, Y.L.1    Li, Z.Y.2    Cao, Y.3    Wan, X.H.4
  • 14
    • 33947402752 scopus 로고    scopus 로고
    • A seventh order numerical method for singular perturbation problems
    • DOI 10.1016/j.amc.2006.08.022, PII S0096300306010083
    • P. Pramod Chakravarthy, K. Phaneendra, and Y.N. Reddy A seventh order numerical method for singular perturbation problems Appl. Math. Comput. 186 2007 860 871 (Pubitemid 46442703)
    • (2007) Applied Mathematics and Computation , vol.186 , Issue.1 , pp. 860-871
    • Chakravarthy, P.P.1    Phaneendra, K.2    Reddy, Y.N.3
  • 15
    • 61749091523 scopus 로고    scopus 로고
    • Initial value technique for singularly perturbed two point boundary value problems using an exponentially fitted finite difference scheme
    • M.K. Kadalbajoo, and D. Kumar Initial value technique for singularly perturbed two point boundary value problems using an exponentially fitted finite difference scheme Comput. Math. Appl. 57 2009 1147 1156
    • (2009) Comput. Math. Appl. , vol.57 , pp. 1147-1156
    • Kadalbajoo, M.K.1    Kumar, D.2
  • 16
    • 0038182679 scopus 로고    scopus 로고
    • Variational approach to the LaneEmden equation
    • J.H. He Variational approach to the LaneEmden equation Appl. Math. Comput. 143 2003 539 541
    • (2003) Appl. Math. Comput. , vol.143 , pp. 539-541
    • He, J.H.1
  • 17
    • 77950626787 scopus 로고    scopus 로고
    • An approximation algorithm for the solution of the nonlinear LaneEmden type equations arising in astrophysics using Hermite functions collocation method
    • K. Parand, Mehdi Dehghan, A.R. Rezaei, and S.M. Ghaderi An approximation algorithm for the solution of the nonlinear LaneEmden type equations arising in astrophysics using Hermite functions 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
  • 18
    • 33751540078 scopus 로고    scopus 로고
    • B-spline solution of singular boundary value problems
    • DOI 10.1016/j.amc.2006.05.035, PII S0096300306004784
    • N. Caglar, and H. Caglar B-spline solution of singular boundary value problems Appl. Math. Comput. 182 2006 1509 1513 (Pubitemid 44838855)
    • (2006) Applied Mathematics and Computation , vol.182 , Issue.2 , pp. 1509-1513
    • Caglar, N.1    Caglar, H.2
  • 19
    • 79955837803 scopus 로고    scopus 로고
    • Application of optimal homotopy asymptotic method for the analytic solution of singular LaneEmden type equation
    • S. Iqbal, and A. Javed Application of optimal homotopy asymptotic method for the analytic solution of singular LaneEmden type equation Appl. Math. Comput. 217 19 2011 7753 7761
    • (2011) Appl. Math. Comput. , vol.217 , Issue.19 , pp. 7753-7761
    • Iqbal, S.1    Javed, A.2
  • 20
    • 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. 70 2009 2480 2484
    • (2009) Nonlinear Anal. , vol.70 , pp. 2480-2484
    • Yildirim, A.1    Zi, T.2
  • 21
    • 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 the 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
  • 22
    • 79955978646 scopus 로고    scopus 로고
    • The variational iteration method for solving nonlinear singular boundary value problems arising in various physical models
    • A.M. Wazwaz The variational iteration method for solving nonlinear singular boundary value problems arising in various physical models Commun. Nonlinear Sci. Numer. Simul. 16 10 2011 3881 3886
    • (2011) Commun. Nonlinear Sci. Numer. Simul. , vol.16 , Issue.10 , pp. 3881-3886
    • Wazwaz, A.M.1
  • 23
    • 78049432455 scopus 로고    scopus 로고
    • Lagrangian method for solving LaneEmden type equation arising in astrophysics on semi-infinite domains
    • K. Parand, A.R. Rezaei, and A. Taghavi Lagrangian method for solving LaneEmden type equation arising in astrophysics on semi-infinite domains Acta Astronaut. 67 2010 673 680
    • (2010) Acta Astronaut. , vol.67 , pp. 673-680
    • Parand, K.1    Rezaei, A.R.2    Taghavi, A.3
  • 24
    • 77950189652 scopus 로고    scopus 로고
    • On the numerical solution of differential equations of LaneEmden type
    • S. Karimi Vanani, and A. Aminataei On the numerical solution of differential equations of LaneEmden type Comput. Math. Appl. 59 2010 2815 2820
    • (2010) Comput. Math. Appl. , vol.59 , pp. 2815-2820
    • Vanani, S.K.1    Aminataei, A.2
  • 25
    • 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 wavelets method for solving differential equations of LaneEmden 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
  • 26
    • 80052264973 scopus 로고    scopus 로고
    • Solving singular initial value problems of EmdenFowler and LaneEmden type
    • V.G. Gupta, and P. Sharma Solving singular initial value problems of EmdenFowler and LaneEmden type Int. J. Appl. Math. Comput. 1 4 2009 206 212
    • (2009) Int. J. Appl. Math. Comput. , vol.1 , Issue.4 , pp. 206-212
    • Gupta, V.G.1    Sharma, P.2
  • 27
    • 72149113334 scopus 로고    scopus 로고
    • Modified variational iteration technique for solving singular fourth-order parabolic partial differential equations
    • M.A. Noor, K.I. Noor, and S.T. Mohyud-Din Modified variational iteration technique for solving singular fourth-order parabolic partial differential equations Nonlinear Anal. 71 2009 e630 e640
    • (2009) Nonlinear Anal. , vol.71
    • Noor, M.A.1    Noor, K.I.2    Mohyud-Din, S.T.3
  • 28
    • 70449630210 scopus 로고    scopus 로고
    • Method for solving nonlinear initial value problems by combining homotopy perturbation and reproducing kernel Hilbert space methods
    • F. Geng, Minggen Cui, and Bo Zhang Method for solving nonlinear initial value problems by combining homotopy perturbation and reproducing kernel Hilbert space methods Nonlinear Anal. RWA 11 2010 637 644
    • (2010) Nonlinear Anal. RWA , vol.11 , pp. 637-644
    • Geng, F.1    Cui, M.2    Zhang, B.3
  • 29
    • 26444543234 scopus 로고    scopus 로고
    • A Taylor polynomial approach for solving differential-difference equations
    • DOI 10.1016/j.cam.2005.02.009, PII S0377042705000993
    • M. Gulsu, and M. Sezer A Taylor polynomial approach for solving differential-difference equations J. Comput. Appl. Math. 186 2006 349 364 (Pubitemid 41433589)
    • (2006) Journal of Computational and Applied Mathematics , vol.186 , Issue.2 , pp. 349-364
    • Gulsu, M.1    Sezer, M.2
  • 30
    • 33644596801 scopus 로고    scopus 로고
    • Taylor polynomial solutions of general linear differential-difference equations with variable coefficients
    • M. Sezer, and A. Akyz-Dacolu Taylor polynomial solutions of general linear differential-difference equations with variable coefficients Appl. Math. Comput. 174 2 2006 1526 1538
    • (2006) Appl. Math. Comput. , vol.174 , Issue.2 , pp. 1526-1538
    • Sezer, M.1    Akyz-Dacolu, A.2
  • 31
    • 80051787613 scopus 로고    scopus 로고
    • A Bessel polynomial approach for solving linear neutral delay differential equations with variable coefficients
    • A Yzba, N. ahin, and M. Sezer A Bessel polynomial approach for solving linear neutral delay differential equations with variable coefficients J. Adv. Res. Differ. Equ. 3 1 2011 81 101
    • (2011) J. Adv. Res. Differ. Equ. , vol.3 , Issue.1 , pp. 81-101
    • Yzba, A.1    Ahin, N.2    Sezer, M.3
  • 32
    • 80052270910 scopus 로고    scopus 로고
    • Bessel matrix method for solving high-order linear Fredholm integro-differential equations
    • Yzba, N. ahin, and M. Sezer Bessel matrix method for solving high-order linear Fredholm integro-differential equations J. Adv. Res. Appl. Math. 3 2 2011 23 47
    • (2011) J. Adv. Res. Appl. Math. , vol.3 , Issue.2 , pp. 23-47
    • Yzba1    Ahin, N.2    Sezer, M.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.