Trigonometric integrators for quasilinear wave equations
Provides a new class of explicit numerical methods for solving quasilinear wave equations, offering stability and error guarantees without restrictive time-step constraints.
The paper introduces trigonometric integrators for quasilinear wave equations, proving second-order convergence for semi-discretization and providing error bounds for a fully discrete scheme without CFL conditions.
Trigonometric time integrators are introduced as a class of explicit numerical methods for quasilinear wave equations. Second-order convergence for the semi-discretization in time with these integrators is shown for a sufficiently regular exact solution. The time integrators are also combined with a Fourier spectral method into a fully discrete scheme, for which error bounds are provided without requiring any CFL-type coupling of the discretization parameters. The proofs of the error bounds are based on energy techniques and on the semiclassical Gårding inequality.