Claudia Wulff’s paper on Runge-Kutta semidiscretizations to appear in Numerische Mathematik

rk-imageThe paper “Runge-Kutta time semidiscretizations of semilinear PDEs with nonsmooth data“, co-authored by Claudia Wulff and Christopher Evans (a former Surrey student) has been accepted for publication in Numerische Mathematik.   In the paper they study semilinear evolution equations posed on a Hilbert space. In particular the semilinear wave equation and nonlinear Schrodinger equation with periodic, Neumann and Dirichlet boundary conditions fit into this framework.  They discretize the evolution equation with an A-stable Runge-Kutta method in time, retaining continuous space, and prove convergence for non-smooth data, extending a result by Brenner and Thomee for linear systems.  Numerical experiments suggest that their estimates are sharp.