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Volumn 44, Issue 4, 2004, Pages 699-709

Energy conservation with non-symplectic methods: Examples and counter-examples

Author keywords

Backward error analysis; Energy conservation; Hamiltonian systems; Symmetric and symplectic methods

Indexed keywords


EID: 18244388472     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10543-004-5240-6     Document Type: Article
Times cited : (75)

References (12)
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    • Benettin, G.1    Giorgilli, A.2
  • 2
    • 84968481790 scopus 로고
    • An algebraic theory of integration methods
    • J. C. Butcher, An algebraic theory of integration methods, Math. Comput., 26 (1972), pp. 79-106.
    • (1972) Math. Comput. , vol.26 , pp. 79-106
    • Butcher, J.C.1
  • 3
    • 0000566698 scopus 로고
    • Backward analysis of numerical integrators and symplectic methods
    • E. Hairer, Backward analysis of numerical integrators and symplectic methods, Annals of Numerical Mathematics, 1 (1994), pp. 107-132.
    • (1994) Annals of Numerical Mathematics , vol.1 , pp. 107-132
    • Hairer, E.1
  • 4
    • 0031505057 scopus 로고    scopus 로고
    • The life-span of backward error analysis for numerical integrators
    • Erratum
    • E. Hairer and C. Lubich, The life-span of backward error analysis for numerical integrators, Numer, Math., 76 (1997), pp. 441-462. Erratum: http://www.unige.ch/math/ folks/hairer/.
    • (1997) Numer, Math. , vol.76 , pp. 441-462
    • Hairer, E.1    Lubich, C.2
  • 5
    • 3142580393 scopus 로고    scopus 로고
    • Symmetric multistep methods over long times
    • E. Hairer and C. Lubich, Symmetric multistep methods over long times, Numer. Math., 97 (2004), pp. 699-723.
    • (2004) Numer. Math. , vol.97 , pp. 699-723
    • Hairer, E.1    Lubich, C.2
  • 6
    • 0013460577 scopus 로고    scopus 로고
    • Geometric numerical integration. Structure-preserving algorithms for ordinary differential equations
    • Springer, Berlin
    • E. Hairer, C. Lubich, and G. Wanner, Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations, Springer Series in Computational Mathematics, Vol. 31, Springer, Berlin, 2002.
    • (2002) Springer Series in Computational Mathematics , vol.31
    • Hairer, E.1    Lubich, C.2    Wanner, G.3
  • 8
    • 0015960381 scopus 로고
    • On the Butcher group and general multi-value methods
    • E. Hairer and G. Wanner, On the Butcher group and general multi-value methods, Computing, 13 (1974), pp. 1-15.
    • (1974) Computing , vol.13 , pp. 1-15
    • Hairer, E.1    Wanner, G.2
  • 10
    • 0026205717 scopus 로고
    • Order conditions for canonical Runge-Kutta schemes
    • J. M. Sanz-Serna and L. Abia, Order conditions for canonical Runge-Kutta schemes, SIAM J. Numer. Anal., 28 (1991), pp. 1081-1096.
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 1081-1096
    • Sanz-Serna, J.M.1    Abia, L.2
  • 12
    • 0036375720 scopus 로고    scopus 로고
    • Non-existence of the modified first integral by symplectic integration methods. II. Kepler problem
    • H. Yoshida, Non-existence of the modified first integral by symplectic integration methods. II. Kepler problem, Celestial Mech. Dynam. Astronom., 83(1-4) (2002), pp. 355-364.
    • (2002) Celestial Mech. Dynam. Astronom. , vol.83 , Issue.1-4 , pp. 355-364
    • Yoshida, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.