Claudia Wulff, Chris Evans
We study semilinear evolution equations [Formula: see text] posed on a Hilbert space [Formula: see text], where A is normal and generates a strongly continuous semigroup, B is a smooth nonlinearity from [Formula: see text] to itself, and [Formula: see text], [Formula: see text], [Formula: see text]. In particular the one-dimensional semilinear wave equation and nonlinear Schrödinger equation with periodic, Neumann and Dirichlet boundary conditions fit into this framework. We discretize the evolution equation with an A-stable Runge-Kutta method in time, retaining continuous space, and prove convergence of order [Formula: see text] for non-smooth initial data [Formula: see text], where [Formula: see text], for a method of classical order p, extending a result by Brenner and Thomée for linear systems...
2016: Numerische Mathematik