Stability and convergence of staggered Runge–Kutta schemes for semilinear wave equations

A staggered Runge–Kutta (staggered RK) scheme is a Runge–Kutta type scheme using a time staggered grid, as proposed by Ghrist et al. in 2000 [6]. Afterwards, Verwer in two papers investigated the efficiency of a scheme proposed by Ghrist et al. [6] for linear wave equations. We study stability and convergence properties of this scheme for semilinear wave equations. In particular, we prove convergence of a fully discrete scheme obtained by applying the staggered RK scheme to the MOL approximation of the equation.