András Bátkai, Petra Csomós, Gregor Nickel
The convergence of various operator splitting procedures, such as the sequential, the Strang and the weighted splitting, is investigated in the presence of a spatial approximation. To this end a variant of Chernoff's product formula is proved. The methods are applied to abstract partial delay differential equations.
András Bátkai, Petra Csomós, Bálint Farkas
We provide a general product formula for the solution of nonautonomous abstract delay equations. After having shown the convergence we obtain estimates on the order of convergence for differentiable history functions. Finally, the theoretical results are demonstrated on some typical numerical examples.
András Bátkai, Petra Csomós, Bálint Farkas et al.
Continuing earlier investigations, we analyze the convergence of operator splitting procedures combined with spatial discretization and rational approximations.
András Bátkai, Petra Csomós, Bálint Farkas
We investigate Lie-Trotter product formulae for abstract nonlinear evolution equations with delay. Using results from the theory of nonlinear contraction semigroups in Hilbert spaces, we explain the convergence of the splitting procedure. The order of convergence is also investigated in detail, and some numerical illustrations are presented.
András Bátkai, Petra Csomós, Klaus-Jochen Engel et al.
We present easy to verify conditions implying stability estimates for operator matrix splittings which ensure convergence of the associated Trotter, Strang and weighted product formulas. The results are applied to inhomogeneous abstract Cauchy problems and to boundary feedback systems.
András Bátkai, Petra Csomós, Bálint Farkas et al.
We provide general product formulas for the solutions of non-autonomous abstract Cauchy problems. The main technical tool is the application of evolution semigroup methods, allowing the direct application of existing results on autonomous problems. The results are then illustrated by the example of a imaginary time Schrödinger equation with time dependent potential. We also obtain convergence rates for the Strang-splitting applied to this problem.