메뉴 건너뛰기




Volumn 14, Issue 12, 2009, Pages 4226-4245

Magnus' expansion for time-periodic systems: Parameter-dependent approximations

Author keywords

Chebyshev polynomials; Magnus expansion; Time periodic systems

Indexed keywords

ITERATIVE METHODS; MATRIX ALGEBRA; NONLINEAR EQUATIONS; ORDINARY DIFFERENTIAL EQUATIONS; POLYNOMIALS; TIME VARYING SYSTEMS;

EID: 67349085340     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2009.02.030     Document Type: Article
Times cited : (20)

References (24)
  • 2
    • 0034273083 scopus 로고    scopus 로고
    • Normal forms and the structure of resonance sets in nonlinear time-periodic systems
    • Butcher E.A., and Sinha S.C. Normal forms and the structure of resonance sets in nonlinear time-periodic systems. Nonlinear Dynam 23 (2000) 35-55
    • (2000) Nonlinear Dynam , vol.23 , pp. 35-55
    • Butcher, E.A.1    Sinha, S.C.2
  • 3
    • 0032157864 scopus 로고    scopus 로고
    • Symbolic computation of local stability and bifurcation surfaces for nonlinear time-periodic systems
    • Butcher E.A., and Sinha S.C. Symbolic computation of local stability and bifurcation surfaces for nonlinear time-periodic systems. Nonlinear Dynam 17 1 (1998) 1-21
    • (1998) Nonlinear Dynam , vol.17 , Issue.1 , pp. 1-21
    • Butcher, E.A.1    Sinha, S.C.2
  • 4
    • 36749044406 scopus 로고    scopus 로고
    • Sufficient conditions for the convergence of the magnus expansion
    • Casas F. Sufficient conditions for the convergence of the magnus expansion. J Phys A: Math Theor 40 (2007) 15001-15017
    • (2007) J Phys A: Math Theor , vol.40 , pp. 15001-15017
    • Casas, F.1
  • 5
    • 0342656703 scopus 로고    scopus 로고
    • Versal deformation and local bifurcation analysis of time-periodic nonlinear systems
    • David A., and Sinha S.C. Versal deformation and local bifurcation analysis of time-periodic nonlinear systems. Nonlinear Dynam 21 (2000) 317-336
    • (2000) Nonlinear Dynam , vol.21 , pp. 317-336
    • David, A.1    Sinha, S.C.2
  • 6
    • 85196206798 scopus 로고
    • Recurrence formulas for homogeneous terms of a convergent series that represents a logarithm of a multiplicative integral on Lie groups
    • Fomenko A.T., and Chakon R.V. Recurrence formulas for homogeneous terms of a convergent series that represents a logarithm of a multiplicative integral on Lie groups. Funktional Anal i Prilozhen 24 1 (1990) 48-58
    • (1990) Funktional Anal i Prilozhen , vol.24 , Issue.1 , pp. 48-58
    • Fomenko, A.T.1    Chakon, R.V.2
  • 7
    • 0002310121 scopus 로고
    • Die symbolische Exponentialformel in der Gruppentheorie. Berichte der Sächsischen Akademie der Wissenschaften
    • Hausdorff F. Die symbolische Exponentialformel in der Gruppentheorie. Berichte der Sächsischen Akademie der Wissenschaften. Math Phys Klasse 58 (1906) 19-48
    • (1906) Math Phys Klasse , vol.58 , pp. 19-48
    • Hausdorff, F.1
  • 8
    • 2542422820 scopus 로고    scopus 로고
    • Expansions that grow on trees
    • Iserles A. Expansions that grow on trees. Not Am Math Soc 49 4 (2002) 430-440
    • (2002) Not Am Math Soc , vol.49 , Issue.4 , pp. 430-440
    • Iserles, A.1
  • 10
    • 84940252991 scopus 로고
    • On the exponential solution of differential equations for a linear operator
    • Magnus W. On the exponential solution of differential equations for a linear operator. Comm Pure Appl Math 7 (1954) 649-673
    • (1954) Comm Pure Appl Math , vol.7 , pp. 649-673
    • Magnus, W.1
  • 11
    • 85196203664 scopus 로고    scopus 로고
    • Mariani J. Exponential solutions of linear differential equations of the second order. PhD thesis, New York University; 1962.
    • Mariani J. Exponential solutions of linear differential equations of the second order. PhD thesis, New York University; 1962.
  • 13
    • 0035578990 scopus 로고    scopus 로고
    • Convergence of the exponential lie series
    • Moan P.C., and Oteo J.A. Convergence of the exponential lie series. J Math Phys 42 (2001) 501-508
    • (2001) J Math Phys , vol.42 , pp. 501-508
    • Moan, P.C.1    Oteo, J.A.2
  • 14
    • 0037354371 scopus 로고    scopus 로고
    • Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later
    • Moler C., and Van Loan C. Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later. SIAM Rev. 45 (2003) 3-49
    • (2003) SIAM Rev. , vol.45 , pp. 3-49
    • Moler, C.1    Van Loan, C.2
  • 15
    • 0039657206 scopus 로고    scopus 로고
    • On the existence of the exponential solution of linear differential systems
    • Oteo J.A., Moan P.C., and Ros J. On the existence of the exponential solution of linear differential systems. J Phys A 32 (1999) 5133-5139
    • (1999) J Phys A , vol.32 , pp. 5133-5139
    • Oteo, J.A.1    Moan, P.C.2    Ros, J.3
  • 16
    • 0002076044 scopus 로고
    • Analysis of time-periodic nonlinear dynamical systems undergoing bifurcations
    • Pandiyan R., and Sinha S.C. Analysis of time-periodic nonlinear dynamical systems undergoing bifurcations. Nonlinear Dynam 8 (1995) 21-43
    • (1995) Nonlinear Dynam , vol.8 , pp. 21-43
    • Pandiyan, R.1    Sinha, S.C.2
  • 18
    • 14944355331 scopus 로고    scopus 로고
    • Control of time-periodic systems via symbolic computation with application to chaos control
    • Sinha S.C., Gowrdon E., and Zhang Y. Control of time-periodic systems via symbolic computation with application to chaos control. Commun Nonlinear Sci Numer Simul 10 (2005) 835-854
    • (2005) Commun Nonlinear Sci Numer Simul , vol.10 , pp. 835-854
    • Sinha, S.C.1    Gowrdon, E.2    Zhang, Y.3
  • 19
    • 0028513255 scopus 로고
    • Analysis of quasilinear dnamical systems with periodic coefficients via Liapunov-Floquet transformation
    • Sinha S.C., and Pandiyan R. Analysis of quasilinear dnamical systems with periodic coefficients via Liapunov-Floquet transformation. Int J Non-linear Mech 29 (1994) 687-702
    • (1994) Int J Non-linear Mech , vol.29 , pp. 687-702
    • Sinha, S.C.1    Pandiyan, R.2
  • 20
    • 0030129491 scopus 로고    scopus 로고
    • Liapunov-Floquet transformation: computation and applications to periodic systems
    • Sinha S.C., Pandiyan R., and Bibb J.S. Liapunov-Floquet transformation: computation and applications to periodic systems. J Vibr Acoust 118 (1996) 209-219
    • (1996) J Vibr Acoust , vol.118 , pp. 209-219
    • Sinha, S.C.1    Pandiyan, R.2    Bibb, J.S.3
  • 21
    • 0031237138 scopus 로고    scopus 로고
    • Symbolic computation of fundamental solution matrices for linear time-periodic dynamical systems
    • Sinha S.C., and Butcher E.A. Symbolic computation of fundamental solution matrices for linear time-periodic dynamical systems. J Sound Vibr 206 1 (1997) 61-85
    • (1997) J Sound Vibr , vol.206 , Issue.1 , pp. 61-85
    • Sinha, S.C.1    Butcher, E.A.2
  • 23
    • 84966255507 scopus 로고
    • On global representations of the solutions of linear differential equations as a product of exponentials
    • Wei J., and Norman E. On global representations of the solutions of linear differential equations as a product of exponentials. Proc Am Math Soc 15 (1964) 327-334
    • (1964) Proc Am Math Soc , vol.15 , pp. 327-334
    • Wei, J.1    Norman, E.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.