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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…
Fourier integrator for periodic NLS: low regularity estimates via discrete Bourgain spaces
Alexander Ostermann, Frédéric Rousset, Katharina Schratz
In this paper, we propose a new scheme for the integration of the periodic nonlinear Schrödinger equation and rigorously prove convergence rates at low regularity. The new integrat…