Analysis and Applied Mathematics Seminar
Chushan Wang
University of Chicago
Error estimates of numerical methods for nonlinear Schrödinger equations with low regularity or singularity
Abstract: The nonlinear Schrödinger equation (NLSE) arises from various applications in quantum physics and chemistry, nonlinear optics, plasma physics, Bose-Einstein Condensates, etc. In these applications, it is necessary to incorporate low-regularity or singularity into the NLSE, which may arise from the potential, nonlinearity, and/or initial data. Typical examples include the discontinuous square-well potential, the singular Coulomb potential, the non-integer power nonlinearity, the logarithmic nonlinearity, and initial data that are ground states of the Schrödinger operator with such potential. Such low regularity and singularity pose significant challenges in the analysis of standard numerical methods and the development of novel accurate, efficient, and structure-preserving numerical schemes.
In this talk, I will introduce several new analysis techniques to establish optimal error bounds for some widely used numerical methods under optimally weak regularity assumptions. Based on the analysis, we also propose novel temporal and spatial discretizations to handle the low regularity and singularity more effectively.
Monday September 8, 2025 at 4:00 PM in 636 SEO