Error analysis of trigonometric integrators for semilinear wave equations
Provides rigorous error bounds for widely used numerical methods in wave equation simulations, benefiting computational scientists needing reliable long-time integration.
The paper proves optimal second-order convergence for trigonometric integrators applied to semilinear wave equations, requiring only finite energy of the exact solution, and shows the analysis is uniform in spatial discretization.
An error analysis of trigonometric integrators (or exponential integrators) applied to spatial semi-discretizations of semilinear wave equations with periodic boundary conditions in one space dimension is given. In particular, optimal second-order convergence is shown requiring only that the exact solution is of finite energy. The analysis is uniform in the spatial discretization parameter. It covers the impulse method which coincides with the method of Deuflhard and the mollified impulse method of García-Archilla, Sanz-Serna & Skeel as well as the trigonometric methods proposed by Hairer & Lubich and by Grimm & Hochbruck. The analysis can also be used to explain the convergence behaviour of the Störmer-Verlet/leapfrog discretization in time.