7 citations · 10 across the 7 of their papers we have counts for
7 papers
Explicit Fourier Integrator for the Periodic dNLS via Gauge Transformation: Low-Regularity Estimates in Discrete Bourgain Spaces
Lun Ji, Hang Li, Alexander Ostermann +1
The derivative nonlinear Schrödinger equation is a fundamental model for the propagation of nonlinear dispersive waves in, for example, plasma physics and nonlinear optics. In this…
A low regularity exponential-type integrator for the derivative nonlinear Schrödinger equation
Lun Ji, Hang Li, Alexander Ostermann
In this work, we present a first-order unfiltered exponential integrator for the one-dimensional derivative nonlinear Schrödinger equation with low regularity. Our analysis shows t…
Highly efficient NURBS-based isogeometric analysis for coupled nonlinear diffusion-reaction equations with and without advection
Ilham Asmouh, Alexander Ostermann
Nonlinear diffusion-reaction systems model a multitude of physical phenomena. A common situation is biological development modeling where such systems have been widely used to stud…
The exponential trapezoidal method for semilinear integro-differential equations
Alexander Ostermann, Nasrin Vaisi
The exponential trapezoidal rule is proposed and analyzed for the numerical integration of semilinear integro-differential equations. Although the method is implicit, the numerical…
Filtered Lie-Trotter splitting for the "good" Boussinesq equation: low regularity error estimates
Lun Ji, Hang Li, Alexander Ostermann +1
We investigate a filtered Lie-Trotter splitting scheme for the ``good" Boussinesq equation and derive an error estimate for initial data with very low regularity. Through the use o…
Low regularity error estimates for high dimensional nonlinear Schrödinger equations
Lun Ji, Alexander Ostermann
The filtered Lie splitting scheme is an established method for the numerical integration of the periodic nonlinear Schrödinger equation at low regularity. Its temporal convergence…
Low regularity full error estimates for the cubic nonlinear Schrödinger equation
Lun Ji, Alexander Ostermann, Frédéric Rousset +1
For the numerical solution of the cubic nonlinear Schrödinger equation with periodic boundary conditions, a pseudospectral method in space combined with a filtered Lie splitting sc…