# Trigonometric integrators for quasilinear wave equations

## TL;DR

This paper introduces explicit trigonometric integrators for quasilinear wave equations, demonstrating second-order convergence and providing error bounds for fully discrete schemes without CFL restrictions.

## Contribution

The paper develops and analyzes a new class of explicit trigonometric integrators for quasilinear wave equations, with proven convergence and error bounds for fully discrete schemes.

## Key findings

- Second-order convergence in semi-discretization in time.
- Error bounds for fully discrete schemes without CFL restrictions.
- Energy techniques and semiclassical Gårding inequality underpin the proofs.

## 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.