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math.NA2021★ 1 cited
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…
math.NA2021
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…
math.NA2021
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…