73 citations · 745 across the 45 of their papers we have counts for
50 papers
Low regularity error estimates for the time integration of 2D NLS
Lun Ji, Alexander Ostermann, Frédéric Rousset +1
A filtered Lie splitting scheme is proposed for the time integration of the cubic nonlinear Schrödinger equation on the two-dimensional torus . The scheme is analyzed…
A robust and conservative dynamical low-rank algorithm
Lukas Einkemmer, Alexander Ostermann, Carmen Scalone
Dynamical low-rank approximation, as has been demonstrated recently, can be extremely efficient in solving kinetic equations. However, a major deficiency is that they do not preser…
Explicit exponential Runge-Kutta methods for semilinear integro-differential equations
Alexander Ostermann, Fardin Saedpanah, Nasrin Vaisi
The aim of this paper is to construct and analyze explicit exponential Runge-Kutta methods for the temporal discretization of linear and semilinear integro-differential equations.…
Exponential integrators for second-order in time partial differential equations
Alexander Ostermann, Duy Phan
Two types of second-order in time partial differential equations (PDEs), namely semilinear wave equations and semilinear beam equations are considered. To solve these equations wit…
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…