Error analysis of implicit Runge-Kutta methods for quasilinear hyperbolic evolution equations

We establish error bounds of implicit Runge-Kutta methods for a class of quasilinear hyperbolic evolution equations including certain Maxwell and wave equations. Our assumptions cover algebraically stable and coercive schemes such as Gauß and Radau collocation methods. We work in a refinement of the analytical setting of Kato\u27s well-posedness theory