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A second order low-regularity integrator for the nonlinear Schrödinger equation
Alexander Ostermann, Fangyan Yao, Yifei Wu
In this paper, we analyse a new exponential-type integrator for the nonlinear cubic Schrödinger equation on the dimensional torus . The scheme has recently also be…
A fully discrete low-regularity integrator for the nonlinear Schrödinger equation
Alexander Ostermann, Fangyan Yao
For the solution of the cubic nonlinear Schrödinger equation in one space dimension, we propose and analyse a fully discrete low-regularity integrator. The scheme is explicit and c…
An exponential integrator/WENO discretization for sonic-boom simulation on modern computer hardware
Lukas Einkemmer, Alexander Ostermann, Mirko Residori
Recently a splitting approach has been presented for the simulation of sonic-boom propagation. Splitting methods allow one to divide complicated partial differential equations into…
Error estimates at low regularity of splitting schemes for NLS
Alexander Ostermann, Frédéric Rousset, Katharina Schratz
We study a filtered Lie splitting scheme for the cubic nonlinear Schrödinger equation. We establish error estimates at low regularity by using discrete Bourgain spaces. This allows…
An efficient second-order energy stable BDF scheme for the space fractional Cahn-Hilliard equation
Yong-Liang Zhao, Meng Li, Alexander Ostermann +1
The space fractional Cahn-Hilliard phase-field model is more adequate and accurate in the description of the formation and phase change mechanism than the classical Cahn-Hilliard m…
A low-rank projector-splitting integrator for the Vlasov--Maxwell equations with divergence correction
Lukas Einkemmer, Alexander Ostermann, Chiara Piazzola
The Vlasov--Maxwell equations are used for the kinetic description of magnetized plasmas. As they are posed in an up to 3+3 dimensional phase space, solving this problem is extreme…