Oscillations over long times in numerical Hamiltonian systems
Ernst Hairer and Christian Lubich
Abstract.
The present survey is concerned with geometric numerical integration with emphasis on theoretical insight for the long-time behaviour of numerical solutions. There are several degrees of difficulty: Non-stiff Hamiltonian systems (backward error analysis); highly oscillatory problems (modulated Fourier expansion); non-linear wave equations. An interesting analogy between highly oscillatory differential equations and linear multistep methods for non-stiff Hamiltonian equations is established.
Key Words.
Geometric numerical integration, Hamiltonian systems, backward error analysis, highly oscillatory problems, modulated Fourier expansion, non-linear wave equations, linear multistep methods.