报告人：王海永教授

报告题目：An efficient spectral method for the one-dimensional fractional Schrodinger equation

报告摘要：

(1) The fractional Schrodinger equation (FSE) arises in a broad range of physical settings and their numerical simulation is challenging due to the nonlocal nature and the power law decay of the solution at infinity. In this talk, we propose a new spectral discretization scheme for the FSE in space using Malmquist-Takenaka functions. We show that this new discretization scheme achieves much better performance than existing discretization schemes in the case where the underlying FSE involves the square root of the Laplacian, while in other cases it also exhibits a comparable or better performance. Numerical experiments are provided to illustrate the performance of the proposed method.

(2) We present a new perspective on error analysis of Legendre approximations for differentiable functions. We start by introducing a sequence of Legendre-Gauss-Lobatto polynomials and prove their theoretical properties, such as an explicit and optimal upper bound. We then apply these properties to derive a new and explicit bound for the Legendre coefficients of differentiable functions and establish some explicit and optimal error bounds for Legendre projections. Illustrative examples are provided to demonstrate the sharpness of our new results.

报告时间：2022年6月18日13:00-16:00

报告形式：腾讯会议；会议号：720-561-308

报告人简介：王海永，2001-2010年于中南大学数学与统计学院本硕博连读，2011-2012年在比利时鲁汶大学（荷语）从事博士后研究，2013年进入华中科技大学数学与统计学院工作至今。主要从事谱方法、高振荡问题高效数值方法等问题的研究，在SIAM J. Numer. Anal.、Numer. Math.、Math. Comp.、IMA J. Numer. Anal.等计算数学知名期刊发表论文二十余篇。