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

摘要

In this paper, we present an error analysis of one-stage explicit extendedRunge--Kutta--Nystr\"{o}m integrators for semilinear wave equations. Theseequations are analysed by using spatial semidiscretizations with periodicboundary conditions in one space dimension. Optimal second-order convergence isproved without requiring Lipschitz continuous and higher regularity of theexact solution. Moreover, the error analysis is not restricted to the spectralsemidiscretization in space.