On energy conservation by trigonometric integrators in the linear case with application to wave equations
Provides a theoretical foundation for energy conservation in numerical integration of oscillatory linear systems, relevant to computational scientists working on wave equations.
The authors derive a modified energy exactly preserved by trigonometric integrators for oscillatory linear Hamiltonian systems under a condition on filter functions, extending known results on all-time near-conservation of energy to linear wave equations.
Trigonometric integrators for oscillatory linear Hamiltonian differential equations are considered. Under a condition of Hairer & Lubich on the filter functions in the method, a modified energy is derived that is exactly preserved by trigonometric integrators. This implies and extends a known result on all-time near-conservation of energy. The extension can be applied to linear wave equations.