计算科学系科学与工程计算论坛

Analysis of Time-Splitting Scheme for the Logarithmic Schrödinger Equation

张晓龙 副教授

（湖南师范大学）

报告时间：2024年4月15日 (星期一) 上午9：30

线上报告: #腾讯会议：335-711-850

报告摘要：The Logarithmic Schrödinger Equation (LogSE) exists rich dynamics and possesses some unique properties when compared to usual Schrödinger equation with cubic nonlinearity.  However, the presence of the logarithmic nonlinear term : f(u) = u ln (|u|^2) poses significant challenge in both numerical solution and error analysis, largely due to the low regularity and singularity. In this talk, we shall characterize such a low regularity in suitable fraction Sobolev space and derive the first set of error estimates for the time-splitting Fourier spectral methods with initial value of fractional order regularity. These new results are supported by recent regularity estimates of the LogSE in PDE community and ample numerical evidence. (Joint Work with Prof. Li-Lian Wang, NTU）

报告人简介：张晓龙，湖南师范大学副教授，2019年博士毕业于大连理工大学。主要研究方向为谱方法和函数数值逼近，目前在SIAM J. Numer. Anal.,  ESAIM: Math. Model. Numer. Anal.,  J. Sci. Comput.,  Sci. China Math. 等杂志上发表论文多篇。

邀请人： 王振 

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