메뉴 건너뛰기




Volumn 36, Issue 5, 1999, Pages 1549-1570

Backward error analysis for numerical integrators

Author keywords

Differential equations; Error analysis; Hamiltonian systems; Long time dynamics; Numerical integrators

Indexed keywords


EID: 0001444647     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142997329797     Document Type: Article
Times cited : (211)

References (41)
  • 4
    • 0010122134 scopus 로고
    • Long-time behaviour of numerically computed orbits: Small and intermediate time-step analysis of one-dimensional systems
    • S. P. AUERBACH, AND A. FRIEDMAN, Long-time behaviour of numerically computed orbits: Small and intermediate time-step analysis of one-dimensional systems, J. Comput. Phys., 93 (1991), pp. 189-223.
    • (1991) J. Comput. Phys. , vol.93 , pp. 189-223
    • Auerbach, S.P.1    Friedman, A.2
  • 5
    • 21344491735 scopus 로고
    • On the Hamiltonian interpolation of near to the identity symplectic mappings with application to symplectic integration algorithms
    • G. BENETTIN AND A. GIORGILLI, On the Hamiltonian interpolation of near to the identity symplectic mappings with application to symplectic integration algorithms, J. Statist. Phys., 74 (1994), pp. 1117-1143.
    • (1994) J. Statist. Phys. , vol.74 , pp. 1117-1143
    • Benettin, G.1    Giorgilli, A.2
  • 6
    • 0000339206 scopus 로고
    • Numerical methods for dynamical systems
    • Clarendon Press, Oxford
    • W.-J. BEYN, Numerical methods for dynamical systems, in Advances in Numerical Analysis, Vol. I, Clarendon Press, Oxford, 1991.
    • (1991) Advances in Numerical Analysis , vol.1
    • Beyn, W.-J.1
  • 8
  • 9
    • 0012031743 scopus 로고
    • Aspects of backward error analysis of numerical ODEs
    • T. EIROLA, Aspects of backward error analysis of numerical ODEs, J. Comput. Appl. Math., 45 (1993), pp. 65-73.
    • (1993) J. Comput. Appl. Math. , vol.45 , pp. 65-73
    • Eirola, T.1
  • 10
    • 0039966698 scopus 로고
    • Formal power series and numerical algorithms for dynamical systems
    • T. Chan and Z.-C. Shi, eds., Ser. Appl. Math. 1, World Scientific, Singapore
    • K. FENG, Formal power series and numerical algorithms for dynamical systems, in Proceedings of International Conference on Scientific Computation, T. Chan and Z.-C. Shi, eds., Ser. Appl. Math. 1, World Scientific, Singapore, 1991, pp. 28-35.
    • (1991) Proceedings of International Conference on Scientific Computation , pp. 28-35
    • Feng, K.1
  • 11
    • 0029691221 scopus 로고    scopus 로고
    • Discretization of homoclinic orbits, rapid forcing, and "invisible" chaos
    • B. FIEDLER AND J. SCHEURLE, Discretization of homoclinic orbits, rapid forcing, and "invisible" chaos, Mem. Amer. Math. Soc., 119 (1996).
    • (1996) Mem. Amer. Math. Soc. , vol.119
    • Fiedler, B.1    Scheurle, J.2
  • 13
    • 0033241472 scopus 로고    scopus 로고
    • Qualitative properties of modified equations
    • O. GONZALEZ, D. J. HIGHAM, AND A. STUART, Qualitative properties of modified equations, IMA J. Numer. Anal., 19 (1999), pp. 169-190.
    • (1999) IMA J. Numer. Anal. , vol.19 , pp. 169-190
    • Gonzalez, O.1    Higham, D.J.2    Stuart, A.3
  • 16
    • 0000566698 scopus 로고
    • Backward analysis of numerical integrators and symplectic methods
    • E. HAIRER, Backward analysis of numerical integrators and symplectic methods, Ann. Numer. Math., 1 (1994), pp. 107-132.
    • (1994) Ann. Numer. Math. , vol.1 , pp. 107-132
    • Hairer, E.1
  • 17
    • 0031270028 scopus 로고    scopus 로고
    • Variable time step integration with symplectic methods
    • E. HAIRER, Variable time step integration with symplectic methods, Appl. Numer. Math., 25 (1997), pp. 219-227.
    • (1997) Appl. Numer. Math. , vol.25 , pp. 219-227
    • Hairer, E.1
  • 18
    • 0031505057 scopus 로고    scopus 로고
    • The life-span of backward error analysis for numerical integrators
    • E. HAIRER AND CH. LUBICH. The life-span of backward error analysis for numerical integrators, Numer. Math., 76 (1997), pp. 441-462.
    • (1997) Numer. Math. , vol.76 , pp. 441-462
    • Hairer, E.1    Lubich, C.H.2
  • 20
    • 0030621833 scopus 로고    scopus 로고
    • Reversible long-term integration with variable stepsizes
    • E. HAIRER AND D. STOFFER, Reversible long-term integration with variable stepsizes, SIAM J. Sci. Comput., 18 (1997), pp. 257-269.
    • (1997) SIAM J. Sci. Comput. , vol.18 , pp. 257-269
    • Hairer, E.1    Stoffer, D.2
  • 21
    • 84966236065 scopus 로고
    • The inverse function theorem of Nash and Moser
    • R. HAMILTON, The inverse function theorem of Nash and Moser, Bull. Amer. Math, Soc., 7 (1982), pp. 65-222.
    • (1982) Bull. Amer. Math, Soc. , vol.7 , pp. 65-222
    • Hamilton, R.1
  • 23
    • 0011615763 scopus 로고
    • Canonical Runge-Kutta methods
    • F. M. LASAGNI, Canonical Runge-Kutta methods, Z. Angew. Math. Phys., 5, 39 (1988), pp. 952-953.
    • (1988) Z. Angew. Math. Phys. , vol.5 , Issue.39 , pp. 952-953
    • Lasagni, F.M.1
  • 24
    • 0002945849 scopus 로고
    • Lectures on Hamiltonian systems
    • J. MOSER, Lectures on Hamiltonian systems, Mem. Amer. Math. Soc., 81 (1968), pp. 1-60.
    • (1968) Mem. Amer. Math. Soc. , vol.81 , pp. 1-60
    • Moser, J.1
  • 25
    • 0021660205 scopus 로고
    • The separation of motions in systems with rapidly rotating phase
    • A. I. NEISHTADT, The separation of motions in systems with rapidly rotating phase, J. Appl. Math. Mech., 48 (1984), pp. 133-139.
    • (1984) J. Appl. Math. Mech. , vol.48 , pp. 133-139
    • Neishtadt, A.I.1
  • 26
    • 0008989198 scopus 로고
    • Numerical Integration of Generalized Euler Equations
    • University of British Columbia, Vancouver, British Columbia, Canada
    • S. REICH, Numerical Integration of Generalized Euler Equations, Tech. Report 93-20, University of British Columbia, Vancouver, British Columbia, Canada, 1993.
    • (1993) Tech. Report 93-20
    • Reich, S.1
  • 28
    • 0031493991 scopus 로고    scopus 로고
    • On higher order semi-explicit symplectic partitioned Runge-Kutta methods for constrained Hamiltonian systems
    • S. REICH, On higher order semi-explicit symplectic partitioned Runge-Kutta methods for constrained Hamiltonian systems, Numer. Math., 76 (1997), pp. 231-247.
    • (1997) Numer. Math. , vol.76 , pp. 231-247
    • Reich, S.1
  • 29
    • 0032755864 scopus 로고    scopus 로고
    • Preservation of adiabatic invariants under symplectic discretization
    • S. REICH, Preservation of adiabatic invariants under symplectic discretization, Appl. Numer. Math., 29 (1999), pp. 45-55.
    • (1999) Appl. Numer. Math. , vol.29 , pp. 45-55
    • Reich, S.1
  • 31
    • 84971897259 scopus 로고
    • Symplectic integrators for Hamiltonian problems: An overview
    • J. M. SANZ-SERNA, Symplectic integrators for Hamiltonian problems: An overview, Acta Numer., 1 (1992), pp. 243-286.
    • (1992) Acta Numer. , vol.1 , pp. 243-286
    • Sanz-Serna, J.M.1
  • 33
    • 0000920052 scopus 로고
    • Rigorous verification of trajectories for the computer simulation of dynamical systems
    • T. SAUER AND J. A. YORK, Rigorous verification of trajectories for the computer simulation of dynamical systems, Nonlinearity, 4 (1994), pp. 961-979.
    • (1994) Nonlinearity , vol.4 , pp. 961-979
    • Sauer, T.1    York, J.A.2
  • 34
    • 0001433845 scopus 로고
    • Symplectic partitioned Runge-Kutta methods
    • G. SUN, Symplectic partitioned Runge-Kutta methods, J. Comput. Math., 11 (1993), pp. 365-372.
    • (1993) J. Comput. Math. , vol.11 , pp. 365-372
    • Sun, G.1
  • 38
    • 49549156305 scopus 로고
    • The modified equation approach to the stability and accuracy of finite-difference methods
    • R. F. WARMING AND B. J. HYETT, The modified equation approach to the stability and accuracy of finite-difference methods, J. Comput. Phys., 14 (1974), pp. 159-179.
    • (1974) J. Comput. Phys. , vol.14 , pp. 159-179
    • Warming, R.F.1    Hyett, B.J.2
  • 39
    • 84966215243 scopus 로고
    • Large deviations in dynamical systems
    • L.-S. YOUNG, Large deviations in dynamical systems, Trans. Amer. Math. Soc., 318 (1990), pp. 525-543.
    • (1990) Trans. Amer. Math. Soc. , vol.318 , pp. 525-543
    • Young, L.-S.1
  • 40
    • 0001005075 scopus 로고
    • Construction of higher order symplectic integrators
    • H. YOSHIDA, Construction of higher order symplectic integrators, Phys. Lett. A, 150 (1990), pp. 262-268.
    • (1990) Phys. Lett. A , vol.150 , pp. 262-268
    • Yoshida, H.1
  • 41
    • 0010254434 scopus 로고
    • Time transformations for the extended phase space
    • K. ZARE AND V. SZEBEHELY, Time transformations for the extended phase space, Celestial Mech., 11 (1975), pp. 469-482.
    • (1975) Celestial Mech. , vol.11 , pp. 469-482
    • Zare, K.1    Szebehely, V.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.