Numerical energy conservation for multi-frequency oscillatory differential equations
Artikel i vetenskaplig tidskrift, 2005

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 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.

Hamiltonian systems

Modulated Fourier expansion

Oscillatory solutions

Störmer-Verlet method

Energy conservation

Gautschi-type numerical methods


David Cohen

Université de Genève

Ernst Hairer

Université de Genève

Christian Lubich

Universität Tübingen

BIT Numerical Mathematics

0006-3835 (ISSN) 1572-9125 (eISSN)

Vol. 45 2 287-305





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