Exponential Integrators for Quasilinear Wave-Type Equations

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.