7 papers
A splitting scheme for the wave maps equation at low regularity
Katie Marsden, Frédéric Rousset, Katharina Schratz
We prove convergence of a filtered Lie splitting scheme for the wave maps equation with low regularity initial data in dimension 3. The convergence analysis is performed in discret…
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 analyze…
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 s…
Time-relaxation structure-preserving explicit low-regularity integrators for the nonlinear Schrödinger equation
Hang Li, Xicui Li, Katharina Schratz +1
We propose and rigorously analyze a novel family of explicit low-regularity exponential integrators for the nonlinear Schrödinger (NLS) equation, based on a time-relaxation framew…
Symmetric resonance based integrators and forest formulae
Yvonne Alama Bronsard, Yvain Bruned, Georg Maierhofer +1
In the present work we introduce a unified framework that allows for the very first systematic construction of symmetric resonance-based integrators to approximate a wide class of…
Resonances and computations
Yvain Bruned, Frédéric Rousset, Katharina Schratz
The computation of time dynamics arising in nonlinear time-dependent partial differential equations is an ongoing challenge in numerical analysis, especially once roughness comes i…