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arXiv · 1702.02981

Trigonometric integrators for quasilinear wave equations

Ludwig Gauckler·Jianfeng Lu·Jeremy L. Marzuola·Frédéric Rousset·Katharina Schratz
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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 G\aa rding inequality.

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Ludwig Gauckler, Jianfeng Lu, Jeremy L. Marzuola, Frédéric Rousset, Katharina Schratz. 2017-02-09. Trigonometric integrators for quasilinear wave equations. https://arxiv.org/abs/1702.02981

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