报告主题：Convergence order of Lie-Trotter operator splitting spectral method for semi-classical fractional Schrödinger equation
报告人：王晚生 教授（上海师范大学）
报告时间：2019 年 11 月 29 日（周五）15:00-16:00
报告地点：校本部 G507
邀请人：胡广大 教授
报告摘要：
In this talk the error estimates are derived for Lie-Trotter operator splitting spectral method for semi-classical fractional Schrödinger equation. We prove local error estimates for the well-known Lie-Trotter splitting operator associated with the linear or nonlinear fractional Schrödinger equation in the semi -classical regime by using a formula for the fractional Laplacian of the product of two functions, when the WKB analysis is valid. The convergence orders of the fully discrete scheme based on Fourier spectral methods for the space approximation are then analyzed and provided with respect to the time step-size ?t and the small (scaled) Planck constant ε for the first time. Numerical studies are reported for several test cases and verify our theoretical results.
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