Operator splitting for delay equations

for the E-valued unknown function u, where E is a Banach space, B is the generator of a (linear) C0-semigroup on E, ut is the history function defined by ut(s) = u(t + s) and Φ is the delay operator. We will employ the semigroup approach on L-phase space (in the spirit of [4] and [5]) to be able to apply numerical splitting schemes to this problem. We prove convergence of theses schemes, investigate their convergence order in various situations: point or distributed delays, and even for nonlinear delay operators (based on [5]). We also intend to present some results for the nonautonomous case, and to present numerical examples as illustration. The talk is based on joint works with András Bátkai, Petra Csomós and Gregor Nickel.