5 papers
Error estimates of time-splitting schemes for nonlinear Klein--Gordon equation with rough data
Lun Ji, Xiaofei Zhao
In this work, we consider the convergence analysis of time-splitting schemes for the nonlinear Klein--Gordon/wave equation under rough initial data. The optimal error bounds of the…
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 thi…
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…
Low-regularity error estimates of a filtered Lie-Trotter splitting scheme for the Zakharov system in arbitrary dimensions
Lun Ji, Hang Li, Chunmei Su
In this paper, we establish error estimates for a fully discrete, filtered Lie splitting scheme applied directly to the Zakharov system -- a model whose solutions may exhibit extre…
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…