Numerical energy conservation for multi-frequency oscillatory differential equations

BIT Numerical Mathematics

Volumn 45, Issue 2, 2005, Pages 287-305

  Cohen, D ^a   Hairer, E ^a   Lubich, Ch ^b  

^a UNIVERSITY OF GENEVA   (Switzerland)

^b UNIVERSITY OF TÜBINGEN   (Germany)

Author keywords

Energy conservation; Gautschi type numerical methods; Hamiltonian systems; Modulated Fourier expansion; Oscillatory solutions; St rmer Verlet method

Indexed keywords

EID: 27144558014     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10543-005-7121-z     Document Type: Article

References (14)

1. G. Benettin, L. Galgani, and A. Giorgilli, Realization of holonomic constraints and freezing of high frequency degrees of freedom in the light of classical perturbation theory. Part I, Comm. Math. Phys., 113 (1987), pp. 87-103.
2. G. Benettin, L. Galgani, and A. Giorgilli, Realization of holonomic constraints and freezing of high frequency degrees of freedom in the light of classical perturbation theory. Part II, Comm. Math. Phys., 121 (1989), pp. 567-601.
3. 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.
4. D. Cohen, E. Hairer, and C. Lubich, Modulated Fourier expansions of highly oscillatory differential equations, Foundations of Comput. Math., 3 (2003), pp. 327-345.
5. P. Deuflhard, A study of extrapolation methods based on multistep schemes without parasitic solutions, Z. Angew. Math. Phys., 30 (1979), pp. 177-189.
6. B. García-Archilla, J. M. Sanz-Serna, and R. D. Skeel, Long-time-step methods for oscillatory differential equations, SIAM J. Sci. Comput., 20 (1999), pp. 930-963.
7. W. Gautschi, Numerical integration of ordinary differential equations based on trigonometric polynomials, Numer. Math., 3 (1961), pp. 381-397.
8. 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/.
9. E. Hairer and C. Lubich, Energy conservation by Störmer-type numerical integrators, in D. F. Griffiths, G. A. Watson (eds), Numerical Analysis 1999, CRC Press LLC, 2000, pp. 169-190.
10. E. Hairer and C. Lubich, Long-time energy conservation of numerical methods for oscillatory differential equations, SIAM J. Numer. Anal., 38 (2000), pp. 414-441.
11. E. Hairer, C. Lubich, and G. Wanner, Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations, Springer Series in Computational Mathematics 31, Springer, Berlin, 2002.
12. M. Hochbruck and C. Lubich, A Gautschi-type method for oscillatory second-order differential equations, Numer. Math., 83 (1999), pp. 403-426.
13. S. Reich, Backward error analysis for numerical integrators, SIAM J. Numer. Anal., 36 (1999), pp. 1549-1570.
14. S. Reich, Preservation of adiabatic invariants under symplectic discretization, Appl. Numer. Math., 29 (1999), pp. 45-55.