11 citations · 16 across the 10 of their papers we have counts for
16 papers
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 framewo…
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…
Computing rough solutions of the stochastic nonlinear wave equation
Jiachuan Cao, Buyang Li, Katharina Schratz
The regularity of solutions to the stochastic nonlinear wave equation plays a critical role in the accuracy and efficiency of numerical algorithms. Rough or discontinuous initial c…
Improved uniform error bounds on a Lawson-type exponential integrator for the long-time dynamics of sine--Gordon equation
Yue Feng, Katharina Schratz
We establish the improved uniform error bounds on a Lawson-type exponential integrator Fourier pseudospectral (LEI-FP) method for the long-time dynamics of sine-Gordon equation whe…
Low regularity integrators for semilinear parabolic equations with maximum bound principles
Cao-Kha Doan, Thi-Thao-Phuong Hoang, Lili Ju +1
This paper is concerned with conditionally structure-preserving, low regularity time integration methods for a class of semilinear parabolic equations of Allen-Cahn type. Important…
A second-order low-regularity correction of Lie splitting for the semilinear Klein--Gordon equation
Buyang Li, Katharina Schratz, Franco Zivcovich
The numerical approximation of the semilinear Klein--Gordon equation in the -dimensional space, with , is studied by analyzing the consistency errors in approximating t…