Error analysis of one-stage explicit extended RKN integrators for semilinear wave equations

In this paper, we present an error analysis of one-stage explicit extended Runge–Kutta–Nystr"{o}m integrators for semilinear wave equations. These equations are analysed by using spatial semidiscretizations with periodic boundary conditions in one space dimension. Optimal second-order convergence is proved without requiring Lipschitz continuous and higher regularity of the exact solution. Moreover, the error analysis is not restricted to the spectral semidiscretization in space.