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Low Regularity Fourier Integrators for Some Nonlinear Dispersive Equations

34f6516e74d33400ff08fe53340128941f2f2d0f

Speaker

Yifei Wu, Center for Applied Mathematics, Tianjin University

Time

2020.11.25 14:00-15:00

Venue

Online—Tencent Meeting APP

Tencent Meeting Info

Conference ID: 899-256-618
Password: 201125

Abstract

Substantial numerical research has been undertaken for solving the nonlinear dispersive equation, and many methods have been developed such as in finite difference methods, operator splitting, spectral methods, discontinuous Galerkin methods and exponential integrators. In recent years, more and more attention has been paid to the low regularity problem based on the practical needs. Exponential integrators have been shown effectively in dealing with low regularity problem.

In this talk, some Fourier integrators are proposed for solving the KdV equation and the nonlinear Schrodinger equation. The designation of the scheme is based on the exponential-type integration and the Phase-Space analysis of the nonlinear dynamics. The schemes are explicit and can be implemented using the fast Fourier transform. By the rigorous analysis, the new schemes provide the first-order or second-order accuracy in Sobolev spaces for rough data, and reduce the regularity requirement of existing methods so far for optimal convergence. Moreover, the conservation laws of the numerical solutions are considered.

Bio

吴奕飞,天津大学应用数学中心教授,博士生导师,国家“万人计划”青年拔尖人才。从事偏微分方程理论和数值计算方面的研究工作,在J. Eur. Math. Soc(JEMS)、Com.Math.Phy.、Adv. Math、Analysis & PDE、Inter. Math. Res. Notice等学术期刊中发表论文,曾主持国家自然科学基金面上项目、青年基金等项目,曾获全国优秀博士论文提名奖。