Trigonometric integrators for quasilinear wave equations

Abstract

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.

33 pages, 2 figures, comments welcome!! Version 3 has updates, typo corrections and simplifications due to referee reports Version 1 contains an extra example removed to shorten the paper overall