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Volumn 13, Issue 10, 2008, Pages 2060-2070

Solving systems of ODEs by homotopy analysis method

Author keywords

Genesio system; Homotopy analysis method; Matrix Riccati differential equation; Nonlinearity; Stiff system

Indexed keywords

APPROXIMATION THEORY; CHAOTIC SYSTEMS; MATRIX ALGEBRA; RICCATI EQUATIONS; RUNGE KUTTA METHODS;

EID: 43049183184     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2007.05.026     Document Type: Article
Times cited : (83)

References (25)
  • 2
    • 20444476600 scopus 로고    scopus 로고
    • GCS of a class of chaotic dynamic systems
    • Park J.H. GCS of a class of chaotic dynamic systems. Chaos Solitons Fractals 26 (2005) 1429-1435
    • (2005) Chaos Solitons Fractals , vol.26 , pp. 1429-1435
    • Park, J.H.1
  • 3
    • 22844452048 scopus 로고    scopus 로고
    • Chaos synchronization between two different chaotic dynamical systems
    • Park J.H. Chaos synchronization between two different chaotic dynamical systems. Chaos Solitons Fractals 27 (2006) 549-554
    • (2006) Chaos Solitons Fractals , vol.27 , pp. 549-554
    • Park, J.H.1
  • 4
    • 0026866475 scopus 로고
    • A harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems
    • Genesio R., and Tesi A. A harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems. Automatica 28 (1992) 531-548
    • (1992) Automatica , vol.28 , pp. 531-548
    • Genesio, R.1    Tesi, A.2
  • 5
    • 4444374711 scopus 로고    scopus 로고
    • Solving Riccati differential equation using Adomian's decomposition method
    • Bahnasawi A.A., El-Tawil M.A., and Abdel-Naby A. Solving Riccati differential equation using Adomian's decomposition method. Appl Math Comput 157 (2004) 503-514
    • (2004) Appl Math Comput , vol.157 , pp. 503-514
    • Bahnasawi, A.A.1    El-Tawil, M.A.2    Abdel-Naby, A.3
  • 9
    • 0031232480 scopus 로고    scopus 로고
    • An approximate solution technique which does not depend upon small parameters (Part 2): an application in fluid mechanics
    • Liao S.J. An approximate solution technique which does not depend upon small parameters (Part 2): an application in fluid mechanics. Int J Nonlinear Mech 32 (1997) 815-822
    • (1997) Int J Nonlinear Mech , vol.32 , pp. 815-822
    • Liao, S.J.1
  • 10
    • 0000494305 scopus 로고    scopus 로고
    • An explicit totally analytic approximation of Blasius viscous flow problems
    • Liao S.J. An explicit totally analytic approximation of Blasius viscous flow problems. Int J Nonlinear Mech 34 (1999) 759-778
    • (1999) Int J Nonlinear Mech , vol.34 , pp. 759-778
    • Liao, S.J.1
  • 11
    • 0141961626 scopus 로고    scopus 로고
    • On the homotopy analysis method for nonlinear problems
    • Liao S.J. On the homotopy analysis method for nonlinear problems. Appl Math Comput 147 (2004) 499-513
    • (2004) Appl Math Comput , vol.147 , pp. 499-513
    • Liao, S.J.1
  • 12
    • 0000615571 scopus 로고
    • An approximate solution technique which does not depend upon small parameters: a special example
    • Liao S.J. An approximate solution technique which does not depend upon small parameters: a special example. Int J Nonlinear Mech 30 (1995) 371-380
    • (1995) Int J Nonlinear Mech , vol.30 , pp. 371-380
    • Liao, S.J.1
  • 13
    • 25844456083 scopus 로고    scopus 로고
    • Comparison between the homotopy analysis method and homotopy perturbation method
    • Liao S.J. Comparison between the homotopy analysis method and homotopy perturbation method. Appl Math Comput 169 (2005) 1186-1194
    • (2005) Appl Math Comput , vol.169 , pp. 1186-1194
    • Liao, S.J.1
  • 14
    • 17944369480 scopus 로고    scopus 로고
    • A new branch of solutions of boundary-layer flows over an impermeable stretched plate
    • Liao S.J. A new branch of solutions of boundary-layer flows over an impermeable stretched plate. Int J Heat Mass Transfer 48 (2005) 2529-3259
    • (2005) Int J Heat Mass Transfer , vol.48 , pp. 2529-3259
    • Liao, S.J.1
  • 15
    • 0141907853 scopus 로고    scopus 로고
    • Explicit analytic solution for similarity boundary layer equations
    • Liao S.J., and Pop I. Explicit analytic solution for similarity boundary layer equations. Int J Heat Mass Transfer 47 (2004) 75-78
    • (2004) Int J Heat Mass Transfer , vol.47 , pp. 75-78
    • Liao, S.J.1    Pop, I.2
  • 16
    • 0041764457 scopus 로고    scopus 로고
    • Exact flow of a third grade fluid past a porous plate using homotopy analysis method
    • Ayub M., Rasheed A., and Hayat T. Exact flow of a third grade fluid past a porous plate using homotopy analysis method. Int J Eng Sci 41 (2003) 2091-2103
    • (2003) Int J Eng Sci , vol.41 , pp. 2091-2103
    • Ayub, M.1    Rasheed, A.2    Hayat, T.3
  • 17
    • 2442526691 scopus 로고    scopus 로고
    • Homotopy analysis of MHD flows of an Oldroyd 8-constant fluid
    • Hayat T., Khan M., and Asghar S. Homotopy analysis of MHD flows of an Oldroyd 8-constant fluid. Acta Mech 167 (2004) 213-232
    • (2004) Acta Mech , vol.167 , pp. 213-232
    • Hayat, T.1    Khan, M.2    Asghar, S.3
  • 18
    • 28144444967 scopus 로고    scopus 로고
    • Homotopy solutions for a generalized second-grade fluid past a porous plate
    • Hayat T., and Khan M. Homotopy solutions for a generalized second-grade fluid past a porous plate. Nonlinear Dyn 42 (2005) 395-405
    • (2005) Nonlinear Dyn , vol.42 , pp. 395-405
    • Hayat, T.1    Khan, M.2
  • 19
    • 36348942985 scopus 로고    scopus 로고
    • Homotopy analysis method for quadratic Riccati differential equation
    • Tan Y, Abbasbandy S. Homotopy analysis method for quadratic Riccati differential equation. Commun Nonlinear Sci Numer Simul doi:10.1016/j.cnsns.2006.03.008.
    • Commun Nonlinear Sci Numer Simul
    • Tan, Y1    Abbasbandy, S.2
  • 20
    • 33750339270 scopus 로고    scopus 로고
    • The application of homotopy analysis method to nonlinear equations arising in heat transfer
    • Abbasbandy S. The application of homotopy analysis method to nonlinear equations arising in heat transfer. Phys Lett A 360 (2006) 109-113
    • (2006) Phys Lett A , vol.360 , pp. 109-113
    • Abbasbandy, S.1
  • 21
    • 35348977016 scopus 로고    scopus 로고
    • The application of homotopy analysis method to solve a generalized Hirota-Satsuma coupled KdV equation
    • Abbasbandy S. The application of homotopy analysis method to solve a generalized Hirota-Satsuma coupled KdV equation. Phys Lett A 15 (2006) 1-6
    • (2006) Phys Lett A , vol.15 , pp. 1-6
    • Abbasbandy, S.1
  • 22
    • 0037440579 scopus 로고    scopus 로고
    • Homotopy perturbation method: a new nonlinear analytical technique
    • He J.H. Homotopy perturbation method: a new nonlinear analytical technique. Appl Math Comput 135 (2003) 73-79
    • (2003) Appl Math Comput , vol.135 , pp. 73-79
    • He, J.H.1
  • 23
    • 43049162263 scopus 로고
    • The decomposition method applied to stiff system
    • Adomian G., Rach R., and Eloed M. The decomposition method applied to stiff system. Math Comp Simul 30 (1988) 271-276
    • (1988) Math Comp Simul , vol.30 , pp. 271-276
    • Adomian, G.1    Rach, R.2    Eloed, M.3
  • 24
    • 0035949880 scopus 로고    scopus 로고
    • Two low accuracy methods for stiff systems
    • Wu X.Y., and Xia J.L. Two low accuracy methods for stiff systems. Appl Math Comput 123 (2001) 141-153
    • (2001) Appl Math Comput , vol.123 , pp. 141-153
    • Wu, X.Y.1    Xia, J.L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.