SIAM Journal on Numerical Analysis, Volume 60, Issue 3, Page 1472-1493, June 2022.
In this paper we propose two exponential integrators of first and second order applied to a class of quasilinear wave-type equations. The analytical framework is an extension of the classical Kato framework and covers quasilinear Maxwell's equations in full space and on a smooth domain as well as a class of quasilinear wave equations. In contrast to earlier works, we do not assume regularity of the solution but only on the data. From this we deduce a well-posedness result upon which we base our error analysis. Compared to existing results, our error bounds require less regularity in space and in time. We include numerical examples to confirm our theoretical findings.

中文翻译：

---

拟线性波型方程的指数积分器

SIAM 数值分析杂志，第 60 卷，第 3 期，第 1472-1493 页，2022 年 6 月
。在本文中，我们提出了两个一阶和二阶指数积分器，应用于一类拟线性波型方程。分析框架是经典加藤框架的扩展，涵盖了全空间和光滑域上的拟线性麦克斯韦方程以及一类拟线性波动方程。与早期的工作相比，我们不假设解决方案的规律性，而只假设数据。由此我们推导出一个适定性结果，我们以此为基础进行误差分析。与现有结果相比，我们的误差界限需要较少的空间和时间规律性。我们包括数值例子来证实我们的理论发现。