Scientific article
Open access

Numerical energy conservation for multi-frequency oscillatory differential equations

Published inBIT, vol. 45, no. 2, p. 287-305
Publication date2005

The long-time near-conservation of the total and oscillatory energies of numerical integrators for Hamiltonian systems with highly oscillatory solutions is studied in this paper. The numerical methods considered are second-order symmetric trigonometric integrators and the Störmer-Verlet method. Previously obtained results for systems with a single high frequency are extended to the multi-frequency case, and new insight into the long-time behaviour of numerical solutions is gained for resonant frequencies. The results are obtained using modulated multi-frequency Fourier expansions and the Hamiltonian-like structure of the modulation system. A brief discussion of conservation properties in the continuous problem is also included.

  • Gautschi-type numerical methods
  • Störmer-Verlet method
  • Hamiltonian systems
  • Modulated Fourier expansion
  • Energy conservation
  • Oscillatory solutions
Citation (ISO format)
COHEN, David, HAIRER, Ernst, LUBICH, Christian. Numerical energy conservation for multi-frequency oscillatory differential equations. In: BIT, 2005, vol. 45, n° 2, p. 287–305. doi: 10.1007/s10543-005-7121-z
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Article (Accepted version)
ISSN of the journal0006-3835

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