English

Trigonometric integrators for quasilinear wave equations

Numerical Analysis 2017-08-28 v3

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.

Keywords

Cite

@article{arxiv.1702.02981,
  title  = {Trigonometric integrators for quasilinear wave equations},
  author = {Ludwig Gauckler and Jianfeng Lu and Jeremy L. Marzuola and Frédéric Rousset and Katharina Schratz},
  journal= {arXiv preprint arXiv:1702.02981},
  year   = {2017}
}

Comments

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

R2 v1 2026-06-22T18:14:19.927Z