메뉴 건너뛰기




Volumn 16, Issue 1, 2011, Pages 112-126

A new application of the homotopy analysis method: Solving the Sturm-Liouville problems

Author keywords

Four point Sturm Liouville problems; Homotopy analysis method; Multiple solutions; Two point Sturm Liouville problems

Indexed keywords

COMPUTATIONAL METHODS; NUMERICAL ANALYSIS;

EID: 77955927814     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2010.04.004     Document Type: Article
Times cited : (97)

References (38)
  • 1
    • 85196208714 scopus 로고
    • The proposed homotopy analysis technique for the solution of nonlinear problems, Ph.D thesis, Shanghai Jiao Tong University
    • Liao SJ. The proposed homotopy analysis technique for the solution of nonlinear problems, Ph.D thesis, Shanghai Jiao Tong University; 1992.
    • (1992)
    • Liao, S.J.1
  • 3
    • 56049106098 scopus 로고    scopus 로고
    • Solving a system of nonlinear fractional partial differential equations using homotopy analysis method
    • Jafari H., Seifi S. Solving a system of nonlinear fractional partial differential equations using homotopy analysis method. Commun Nonlinear Sci Numer Simulat 2009, 14:1962-1969.
    • (2009) Commun Nonlinear Sci Numer Simulat , vol.14 , pp. 1962-1969
    • Jafari, H.1    Seifi, S.2
  • 5
    • 38849190109 scopus 로고    scopus 로고
    • Analysis of a time fractional wave-like equation with the homotopy analysis method
    • Xu H., Cang J. Analysis of a time fractional wave-like equation with the homotopy analysis method. Phys Lett A 2008, 372:1250-1255.
    • (2008) Phys Lett A , vol.372 , pp. 1250-1255
    • Xu, H.1    Cang, J.2
  • 6
    • 61449254412 scopus 로고    scopus 로고
    • The series solution of problems in the calculus of variations via the homotopy analysis method
    • Abbasbandy S., Shirzadi A. The series solution of problems in the calculus of variations via the homotopy analysis method. Z Naturforsch A 2009, 64:30-36.
    • (2009) Z Naturforsch A , vol.64 , pp. 30-36
    • Abbasbandy, S.1    Shirzadi, A.2
  • 7
    • 56049110221 scopus 로고    scopus 로고
    • Adaptation of homotopy analysis method for the numeric-analytic solution of Chen system
    • Alomari A.K., Noorani M.S.M., Nazar R. Adaptation of homotopy analysis method for the numeric-analytic solution of Chen system. Commun Nonlinear Sci Numer Simulat 2009, 4:2336-2346.
    • (2009) Commun Nonlinear Sci Numer Simulat , vol.4 , pp. 2336-2346
    • Alomari, A.K.1    Noorani, M.S.M.2    Nazar, R.3
  • 8
    • 9544236204 scopus 로고    scopus 로고
    • Solving the one-loop soliton solution of the Vakhnenko equation by means of the Homotopy analysis method
    • Wu Y., Wang C., Liao S.J. Solving the one-loop soliton solution of the Vakhnenko equation by means of the Homotopy analysis method. Chaos Solitons Fractals 2005, 23:1733-1740.
    • (2005) Chaos Solitons Fractals , vol.23 , pp. 1733-1740
    • Wu, Y.1    Wang, C.2    Liao, S.J.3
  • 9
    • 41649091786 scopus 로고    scopus 로고
    • The application of homotopy analysis method for 2-dimensional steady slip flow in microchannels
    • Zhang T.T., Jia L., Wang Z.C., Li X. The application of homotopy analysis method for 2-dimensional steady slip flow in microchannels. Phys Lett A 2008, 372:3223-3227.
    • (2008) Phys Lett A , vol.372 , pp. 3223-3227
    • Zhang, T.T.1    Jia, L.2    Wang, Z.C.3    Li, X.4
  • 10
    • 42949165898 scopus 로고    scopus 로고
    • The application of homotopy analysis method to thin film flows of a third order fluid
    • Sajid M., Hayat T. The application of homotopy analysis method to thin film flows of a third order fluid. Chaos Solitons Fractals 2008, 38:506-515.
    • (2008) Chaos Solitons Fractals , vol.38 , pp. 506-515
    • Sajid, M.1    Hayat, T.2
  • 11
    • 52049104657 scopus 로고    scopus 로고
    • Generalizing homotopy analysis method to solve LotkaVolterra equation
    • Zou L., Zong Z., Dong G.H. Generalizing homotopy analysis method to solve LotkaVolterra equation. Comput Math Appl 2008, 9:2289-2293.
    • (2008) Comput Math Appl , vol.9 , pp. 2289-2293
    • Zou, L.1    Zong, Z.2    Dong, G.H.3
  • 12
    • 67349180749 scopus 로고    scopus 로고
    • Numerical solution of the generalized Zakharov equation by homotopy analysis method
    • Abbasbandy S., Babolian E., Ashtiani M. Numerical solution of the generalized Zakharov equation by homotopy analysis method. Commun Nonlinear Sci Numer Simulat 2009, 14:4114-4121.
    • (2009) Commun Nonlinear Sci Numer Simulat , vol.14 , pp. 4114-4121
    • Abbasbandy, S.1    Babolian, E.2    Ashtiani, M.3
  • 13
    • 56549119386 scopus 로고    scopus 로고
    • The homotopy analysis method to solve the Burgers-Huxley equation
    • Molabahrami A., Khani F. The homotopy analysis method to solve the Burgers-Huxley equation. Nonlinear Anal Real World Appl 2009, 10:589-600.
    • (2009) Nonlinear Anal Real World Appl , vol.10 , pp. 589-600
    • Molabahrami, A.1    Khani, F.2
  • 14
    • 41449097382 scopus 로고    scopus 로고
    • Series solutions of nano boundary layer flows by means of the homotopy analysis method
    • Cheng J., Liao S.J., Mohapatra R.N., Vajravelu K. Series solutions of nano boundary layer flows by means of the homotopy analysis method. J Math Anal Appl 2008, 343:233-245.
    • (2008) J Math Anal Appl , vol.343 , pp. 233-245
    • Cheng, J.1    Liao, S.J.2    Mohapatra, R.N.3    Vajravelu, K.4
  • 15
    • 67349169966 scopus 로고    scopus 로고
    • On the selection of auxiliary functions, operators, and convergence control parameters in the application of the Homotopy Analysis Method to nonlinear differential equations: a general approach
    • Van Gorder R.A., Vajravelu K. On the selection of auxiliary functions, operators, and convergence control parameters in the application of the Homotopy Analysis Method to nonlinear differential equations: a general approach. Commun Nonlinear Sci Numer Simulat 2009, 14:4078-4089.
    • (2009) Commun Nonlinear Sci Numer Simulat , vol.14 , pp. 4078-4089
    • Van Gorder, R.A.1    Vajravelu, K.2
  • 16
    • 55549136027 scopus 로고    scopus 로고
    • Notes on the homotopy analysis method: some definitions and theorems
    • Liao S.J. Notes on the homotopy analysis method: some definitions and theorems. Commun Nonlinear Sci Numer Simulat 2009, 14:983-997.
    • (2009) Commun Nonlinear Sci Numer Simulat , vol.14 , pp. 983-997
    • Liao, S.J.1
  • 17
    • 72049102345 scopus 로고    scopus 로고
    • On the relationship between the homotopy analysis method and Euler transform
    • Liao S.J. On the relationship between the homotopy analysis method and Euler transform. Commun Nonlinear Sci Numer Simulat 2010, 15:1421-1431.
    • (2010) Commun Nonlinear Sci Numer Simulat , vol.15 , pp. 1421-1431
    • Liao, S.J.1
  • 18
    • 62949170767 scopus 로고    scopus 로고
    • A new method for homoclinic solutions of ordinary differential equations
    • Talay Akyildiz F., Vajravelu K., Liao S.J. A new method for homoclinic solutions of ordinary differential equations. Chaos Solitons Fractals 2009, 39:1073-1082.
    • (2009) Chaos Solitons Fractals , vol.39 , pp. 1073-1082
    • Talay Akyildiz, F.1    Vajravelu, K.2    Liao, S.J.3
  • 19
    • 56049098395 scopus 로고    scopus 로고
    • Investigation of a powerful analytical method into natural convection boundary layer flow
    • Ghotbi A.R., Bararnia H., Domairry G., Barari A. Investigation of a powerful analytical method into natural convection boundary layer flow. Commun Nonlinear Sci Numer Simulat 2009, 14:2222-2228.
    • (2009) Commun Nonlinear Sci Numer Simulat , vol.14 , pp. 2222-2228
    • Ghotbi, A.R.1    Bararnia, H.2    Domairry, G.3    Barari, A.4
  • 20
    • 38949143275 scopus 로고    scopus 로고
    • Analytic solution for flow of Sisko fluid through a porous medium Authors
    • Khan M., Abbas Z., Hayat T. Analytic solution for flow of Sisko fluid through a porous medium Authors. Trans Porous Media 2008, 71:23-37.
    • (2008) Trans Porous Media , vol.71 , pp. 23-37
    • Khan, M.1    Abbas, Z.2    Hayat, T.3
  • 21
    • 63449089713 scopus 로고    scopus 로고
    • Solution of the MHD Falkner-Skan flow by homotopy analysis method
    • Abbasbandy S., Hayat T. Solution of the MHD Falkner-Skan flow by homotopy analysis method. Commun Nonlinear Sci Numer Simulat 2009, 14:3591-3598.
    • (2009) Commun Nonlinear Sci Numer Simulat , vol.14 , pp. 3591-3598
    • Abbasbandy, S.1    Hayat, T.2
  • 22
    • 35348973440 scopus 로고    scopus 로고
    • Solutions of time-dependent Emden-Fowler type equations by homotopy analysis method
    • Bataineh A.S., Noorani M.S.M., Hashim I. Solutions of time-dependent Emden-Fowler type equations by homotopy analysis method. Phys Lett A 2007, 371:72-82.
    • (2007) Phys Lett A , vol.371 , pp. 72-82
    • Bataineh, A.S.1    Noorani, M.S.M.2    Hashim, I.3
  • 23
    • 50349103358 scopus 로고    scopus 로고
    • Analytic and numerical solutions to the Lane-Emden equation
    • Van Gorder R.A., Vajravelu K. Analytic and numerical solutions to the Lane-Emden equation. Phys Lett A 2008, 372:6060-6065.
    • (2008) Phys Lett A , vol.372 , pp. 6060-6065
    • Van Gorder, R.A.1    Vajravelu, K.2
  • 24
    • 34347339334 scopus 로고    scopus 로고
    • Application of homotopy analysis method to fractional KdV-Burgers-Kuramoto equation
    • Song L., Zhang H. Application of homotopy analysis method to fractional KdV-Burgers-Kuramoto equation. Phys Lett A 2007, 367:88-94.
    • (2007) Phys Lett A , vol.367 , pp. 88-94
    • Song, L.1    Zhang, H.2
  • 25
    • 67349162538 scopus 로고    scopus 로고
    • Comparison of homotopy analysis method and homotopy perturbation method through an evolution equation
    • Liang S., Jeffrey D.J. Comparison of homotopy analysis method and homotopy perturbation method through an evolution equation. Commun Nonlinear Sci Numer Simulat 2009, 14:4057-4064.
    • (2009) Commun Nonlinear Sci Numer Simulat , vol.14 , pp. 4057-4064
    • Liang, S.1    Jeffrey, D.J.2
  • 26
    • 63449128519 scopus 로고    scopus 로고
    • The homotopy analysis method for multiple solutions of nonlinear boundary value problems
    • Abbasbandy S., Magyari E., Shivanian E. The homotopy analysis method for multiple solutions of nonlinear boundary value problems. Commun Nonlinear Sci Numer Simulat 2009, 14:3530-3536.
    • (2009) Commun Nonlinear Sci Numer Simulat , vol.14 , pp. 3530-3536
    • Abbasbandy, S.1    Magyari, E.2    Shivanian, E.3
  • 27
    • 26044465275 scopus 로고    scopus 로고
    • The Adomian decomposition method for computing eigenelements of Sturm-Liouville two point boundary value problems
    • Attili B.S. The Adomian decomposition method for computing eigenelements of Sturm-Liouville two point boundary value problems. Appl Math Comput 2005, 168:1306-1316.
    • (2005) Appl Math Comput , vol.168 , pp. 1306-1316
    • Attili, B.S.1
  • 28
    • 67349195816 scopus 로고    scopus 로고
    • Variational iteration method for Sturm-Liouville differential equations
    • Altintan D., Uĝura Ö. Variational iteration method for Sturm-Liouville differential equations. Comput Math Appl 2009, 58:322-328.
    • (2009) Comput Math Appl , vol.58 , pp. 322-328
    • Altintan, D.1    Uĝura, Ö.2
  • 29
    • 33751512653 scopus 로고    scopus 로고
    • An efficient method for computing eigenelements of Sturm-Liouville fourth-order boundary value problems
    • Attili B.S., Lesnic D. An efficient method for computing eigenelements of Sturm-Liouville fourth-order boundary value problems. Appl Math Comput 2006, 182:1247-1254.
    • (2006) Appl Math Comput , vol.182 , pp. 1247-1254
    • Attili, B.S.1    Lesnic, D.2
  • 30
    • 62549132486 scopus 로고    scopus 로고
    • An efficient technique for finding the eigenvalues of fourth-order Sturm-Liouville problems
    • Syam M.I., Siyyam H.I. An efficient technique for finding the eigenvalues of fourth-order Sturm-Liouville problems. Chaos Solitons Fractals 2009, 39:659-665.
    • (2009) Chaos Solitons Fractals , vol.39 , pp. 659-665
    • Syam, M.I.1    Siyyam, H.I.2
  • 31
    • 61749099595 scopus 로고    scopus 로고
    • Series solution of nonlinear eigenvalue problems by means of the homotopy analysis method
    • Liao S.J. Series solution of nonlinear eigenvalue problems by means of the homotopy analysis method. Nonlinear Anal Real World Appl 2009, 10:2455-2470.
    • (2009) Nonlinear Anal Real World Appl , vol.10 , pp. 2455-2470
    • Liao, S.J.1
  • 32
    • 84952401788 scopus 로고
    • On the existence of positive solutions of fourth order ordinary differential equation
    • Ma R.Y., Wang H.Y. On the existence of positive solutions of fourth order ordinary differential equation. Appl Anal 1995, 59:225-231.
    • (1995) Appl Anal , vol.59 , pp. 225-231
    • Ma, R.Y.1    Wang, H.Y.2
  • 33
    • 0021371823 scopus 로고
    • Fourth-order two-point boundary value problems; estimates by two side bounds
    • Schroder J. Fourth-order two-point boundary value problems; estimates by two side bounds. Nonlinear Anal 1984, 8:107-144.
    • (1984) Nonlinear Anal , vol.8 , pp. 107-144
    • Schroder, J.1
  • 34
    • 5844393936 scopus 로고
    • Iterative methods for a fourth order boundary value problem
    • Agarwal R.P., Chow M.Y. Iterative methods for a fourth order boundary value problem. J Comput Appl Math 1984, 10:203-217.
    • (1984) J Comput Appl Math , vol.10 , pp. 203-217
    • Agarwal, R.P.1    Chow, M.Y.2
  • 35
    • 33947175349 scopus 로고
    • On the fourth-order boundary value problems arising in beam analysis
    • Agarwal R.P. On the fourth-order boundary value problems arising in beam analysis. Diff Integral Equat 1989, 2:91-110.
    • (1989) Diff Integral Equat , vol.2 , pp. 91-110
    • Agarwal, R.P.1
  • 36
    • 0002872438 scopus 로고
    • Solvability of some fourth (and higher) order singular boundary value problems
    • O'Regan D. Solvability of some fourth (and higher) order singular boundary value problems. J Math Anal Appl 1991, 161:78-116.
    • (1991) J Math Anal Appl , vol.161 , pp. 78-116
    • O'Regan, D.1
  • 37
    • 38249027575 scopus 로고
    • Existence and uniqueness theorems for a bending of an elastic beam equation at resonance
    • Gupta C.P. Existence and uniqueness theorems for a bending of an elastic beam equation at resonance. J Math Anal Appl 1988, 135:208-225.
    • (1988) J Math Anal Appl , vol.135 , pp. 208-225
    • Gupta, C.P.1
  • 38
    • 33750630894 scopus 로고    scopus 로고
    • Positive solutions of fourth-order nonlinear singular Sturm-Liouville eigenvalue problems
    • Liu L., Zhang X., Wu Y. Positive solutions of fourth-order nonlinear singular Sturm-Liouville eigenvalue problems. J Math Anal Appl 2007, 326:1212-1224.
    • (2007) J Math Anal Appl , vol.326 , pp. 1212-1224
    • Liu, L.1    Zhang, X.2    Wu, Y.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.