2017/02/09 by Gauckler, Ludwig, Lu, Jianfeng, Marzuola, Jeremy L. +2
#65L70 #65M15 #65M20 #65P10 #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.1702.02981
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.