On Energy Conservation by Trigonometric Integrators in the Linear Case with Application to Wave Equations (Journal of Computational Mathematics, 2020)
Trigonometric integrators for oscillatory linear Hamiltonian differential equations areconsidered. 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. Thisimplies and extends a known result on all-time near-conservation of energy. The extensioncan be applied to linear wave equations.