Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	苏春梅助理教授，清华大学丘成桐数学科学中心
Inviter:	张硕副研究员
Title:	Regularized numerical methods and analysis for the logarithmic Schrodinger equation
Time & Venue:	2021.10.12 10:00-11:00 科技综合楼311教室
Abstract:	We propose some regularized models for the singular logarithmic Schr?dinger equation (LogSE) and establish the error bounds. In order to suppress the round-off error and to avoid the blow-up of the logarithmic nonlinearity, some regularized logarithmic Schr?dinger equations (RLogSE) are proposed with a small regularization parameter $0 < \varepsilon \le 1$ and linear convergence is established between the solutions of RLogSE and LogSE in terms of $\varepsilon$. Then we use the first-order splitting integrator to solve the regularized model and establish a nontrivial error bound $O(\tau^{1/2}\ln(\varepsilon^{-1}))$ with $\tau>0$ the time step, which implies an error bound at $O(\varepsilon+ \tau^{1/2}\ln(\varepsilon^{-1}))$ for the LogSE by the Lie-Trotter splitting method. Numerical results are reported to confirm the error bounds and to demonstrate rich and complicated dynamics of the LogSE