报告题目： Multiple relaxation Runge–Kutta methods for the nonlinear Gross-Pitaevskii equations

报 告 人：李东方 教授 （华中科技大学）

邀 请 人：宋怀玲

报告时间：2025/10/25 周六 9:00-10:00

报告地点：数学院207

摘    要：

A novel class of stabilized multiple-relaxation implicit-explicit Runge-Kutta methods is proposed for solving nonlinear Gross-Pitaevskii equations. The methods conserve the mass and the energy simultaneously in the discrete sense, and achieve arbitrarily high-order accuracy in the temporal direction. Additionally, there are several highlights in this study. Firstly, this is the first attempt to apply the stabilization approach to develop relaxation-type schemes, which effectively avoids the blow-up of the relaxation parameters due to the nonlinearity and stiffness of the problems. Secondly, the governing equations that determine the relaxation parameters are newly designed to conserve the original invariants, which can be extended to conserve more invariants of other physical models. Thirdly, the schemes are linearly implicit after obtaining the relaxation parameters, and thus are easy to implement. Several numerical experiments are carried out to confirm the effectiveness and theoretical results of the proposed methods.

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），国家级青年人才计划入选者，香江学者奖。主持国家自然科学基金2项，科技部课题3项，参与国家自然科学基金重点项目1项和863课题1项，主要从事偏微分方程数值解、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研究上取得了有意义的研究进展。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数学SCI期刊上，且有多篇高被引论文。

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