73 citations · 745 across the 45 of their papers we have counts for
5 papers · 2 filters
A comparison of boundary correction methods for Strang splitting
Lukas Einkemmer, Alexander Ostermann
In this paper we consider splitting methods in the presence of non-homogeneous boundary conditions. In particular, we consider the corrections that have been described and analyzed…
Splitting methods for constrained diffusion-reaction systems
Robert Altmann, Alexander Ostermann
We consider Lie and Strang splitting for the time integration of constrained partial differential equations with a nonlinear reaction term. Since such systems are known to be sensi…
A splitting approach for the magnetic Schrödinger equation
Marco Caliari, Alexander Ostermann, Chiara Piazzola
The Schrödinger equation in the presence of an external electromagnetic field is an important problem in computational quantum mechanics. It also provides a nice example of a diffe…
Low regularity exponential-type integrators for semilinear Schrödinger equations
Alexander Ostermann, Katharina Schratz
We introduce low regularity exponential-type integrators for nonlinear Schrödinger equations for which first-order convergence only requires the boundedness of one additional deriv…
Overcoming order reduction in diffusion-reaction splitting. Part 2: oblique boundary conditions
Lukas Einkemmer, Alexander Ostermann
Splitting methods constitute a well-established class of numerical schemes for the time integration of partial differential equations. Their main advantages over more traditional s…