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Volumn 34, Issue 4, 1997, Pages 1391-1417

Error growth in the numerical integration of periodic orbits, with application to Hamiltonian and reversible systems

Author keywords

Asymptotic expansion of the error; Conservation of energy; Error growth; Hamiltonian systems; Periodic solutions; Reversible systems; Runge Kutta methods; Symplectic integrators

Indexed keywords


EID: 0001185008     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142995281152     Document Type: Article
Times cited : (51)

References (28)
  • 3
    • 0001500810 scopus 로고
    • On invariant closed curves for one-step methods
    • W.-J. BEYN, On invariant closed curves for one-step methods, Numer. Math., 51 (1987), pp. 103-122.
    • (1987) Numer. Math. , vol.51 , pp. 103-122
    • Beyn, W.-J.1
  • 5
    • 0028751373 scopus 로고
    • Some orbital test problems
    • J. C. BUTCHER, Some orbital test problems, Computing, 53 (1994), pp. 75-94.
    • (1994) Computing , vol.53 , pp. 75-94
    • Butcher, J.C.1
  • 6
    • 0003103904 scopus 로고
    • Accurate long-term integration of dynamical systems
    • M. P. CALVO AND E. HAIRER, Accurate long-term integration of dynamical systems, Appl. Numer. Math., 18 (1995), pp. 95-105.
    • (1995) Appl. Numer. Math. , vol.18 , pp. 95-105
    • Calvo, M.P.1    Hairer, E.2
  • 7
    • 0000622670 scopus 로고
    • The development of variable-step symplectic integrators, with application to the two-body problem
    • M. P. CALVO AND J. M. SANZ-SERNA, The development of variable-step symplectic integrators, with application to the two-body problem, SIAM J. Sci. Comput., 14 (1993), pp. 936-952.
    • (1993) SIAM J. Sci. Comput. , vol.14 , pp. 936-952
    • Calvo, M.P.1    Sanz-Serna, J.M.2
  • 10
    • 0023833412 scopus 로고
    • Invariant curves of one-step methods
    • T. EIROLA, Invariant curves of one-step methods, BIT, 28 (1988), pp. 113-122.
    • (1988) BIT , vol.28 , pp. 113-122
    • Eirola, T.1
  • 11
    • 38249021498 scopus 로고
    • Two concepts for numerical periodic solutions of ODE's
    • T. EIROLA, Two concepts for numerical periodic solutions of ODE's, Appl. Math. Comput., 31 (1989), pp. 121-131.
    • (1989) Appl. Math. Comput. , vol.31 , pp. 121-131
    • Eirola, T.1
  • 12
    • 0012031743 scopus 로고
    • Aspects of backward error analysis for numerical ODEs
    • T. EIROLA, Aspects of backward error analysis for numerical ODEs, J. Comput. Appl. Math., 45 (1993), pp. 65-73.
    • (1993) J. Comput. Appl. Math. , vol.45 , pp. 65-73
    • Eirola, T.1
  • 13
    • 0007057264 scopus 로고
    • The rate of error growth in Hamiltonian-conserving integrators
    • D. J. ESTEP AND A. M. STUART, The rate of error growth in Hamiltonian-conserving integrators, Z. Angew. Math. Phys., 46 (1995), pp. 407-418.
    • (1995) Z. Angew. Math. Phys. , vol.46 , pp. 407-418
    • Estep, D.J.1    Stuart, A.M.2
  • 14
    • 0013176317 scopus 로고
    • Erring and being conservative
    • D. F. Griffiths and G. A. Watson, eds., Longman Press, London
    • J. DE FRUTOS AND J. M. SANZ-SERNA, Erring and being conservative, in Numerical Analysis 1993, D. F. Griffiths and G. A. Watson, eds., Longman Press, London, 1994, pp. 75-88.
    • (1994) Numerical Analysis 1993 , pp. 75-88
    • De Frutos, J.1    Sanz-Serna, J.M.2
  • 15
    • 0031540242 scopus 로고    scopus 로고
    • Accuracy and conservation properties in numerical integration: The case of the Korteweg-de Vries equation
    • J. DE FRUTOS AND J. M. SANZ-SERNA, Accuracy and conservation properties in numerical integration: The case of the Korteweg-de Vries equation, Numer. Math., 75 (1997), pp. 421-445.
    • (1997) Numer. Math. , vol.75 , pp. 421-445
    • De Frutos, J.1    Sanz-Serna, J.M.2
  • 19
    • 0347360627 scopus 로고
    • Some aspects of the dynamics and numerics of Hamiltonian systems
    • D. D. Broomhead and A. Iserles, eds., Clarendon Press, Oxford
    • R. S. MACKAY, Some aspects of the dynamics and numerics of Hamiltonian systems, in The Dynamics of Numerics and the Numerics of Dynamics, D. D. Broomhead and A. Iserles, eds., Clarendon Press, Oxford, 1992, pp. 137-193.
    • (1992) The Dynamics of Numerics and the Numerics of Dynamics , pp. 137-193
    • MacKay, R.S.1
  • 20
    • 0026847865 scopus 로고
    • An explicit Runge-Kutta-Nyström method is canonical if and only if its adjoint is explicit
    • D. OKUNBOR AND R. D. SKEEL, An explicit Runge-Kutta-Nyström method is canonical if and only if its adjoint is explicit, SIAM J. Numer. Anal., 29 (1992), pp. 521-527.
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 521-527
    • Okunbor, D.1    Skeel, R.D.2
  • 21
    • 0009402551 scopus 로고
    • Lack of dissipativity is not symplecticness
    • A. PORTILLO AND J. M. SANZ-SERNA, Lack of dissipativity is not symplecticness, BIT, 35 (1995), pp. 269-276.
    • (1995) BIT , vol.35 , pp. 269-276
    • Portillo, A.1    Sanz-Serna, J.M.2
  • 26
    • 0011813479 scopus 로고
    • On Reversible and Canonical Integration Methods
    • Applied Mathematics, Eidgenoessische Technische Hochsshule (ETH), Zürich
    • D. STOFFER, On Reversible and Canonical Integration Methods, Res. report no. 88-05, Applied Mathematics, Eidgenoessische Technische Hochsshule (ETH), Zürich, 1988.
    • (1988) Res. Report No. 88-05 , vol.88 , Issue.5
    • Stoffer, D.1
  • 27
    • 0029229318 scopus 로고
    • Variable steps for reversible integration methods
    • D. STOFFER, Variable steps for reversible integration methods, Computing, 55 (1995), pp. 1-22.
    • (1995) Computing , vol.55 , pp. 1-22
    • Stoffer, D.1
  • 28
    • 0000180095 scopus 로고
    • Invariant curves for variable step size integrators
    • D. STOFFER AND K. NIPP, Invariant curves for variable step size integrators, BIT, 31 (1991), pp. 169-180.
    • (1991) BIT , vol.31 , pp. 169-180
    • Stoffer, D.1    Nipp, K.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.