勷勤数学•专家报告

题      目：High-order structure-preserving Runge-Kutta methods for the nonlinear schrodinger equation

报  告  人：李东方 教授  (邀请人：邹为)

                                              华中科技大学       

时      间：3月25日  16：00-17：00

地     点：数科院东楼401

报告人简介:

        李东方，华中科技大学数学与统计学院教授，博导，国家级青年人才。主持国家级课题6项。主要从事微分方程数值解、机器学习和信号处理等领域的研究工作。尤其在微分方程保结构算法和分数阶微分方程的高效数值算法和理论上取得一些有意义的进展。相关工作发表在《SIAM. J. Numer. Anal.》，《SIAM. J. Sci. Comput.》、《Math. Comput》、《J. Comp. Phys.》等多个国际著名计算学科SCI期刊上，多篇为高被引论文。

摘      要：

      A novel family of high-order structure-preserving methods is proposed for the nonlinear Schrodinger equation. The methods are developed by applying the multiple relaxation idea to the different Runge--Kutta methods. It is shown that the multiple relaxation  Runge--Kutta methods can achieve high-order accuracy in time and preserve multiple original invariants atthe discrete level. Several numerical experiments are carried out to support the theoretical results and illustrate theeffectiveness and efficiency of the proposed methods.

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