Lecture Content：

A novel family of high-order structure-preserving methods is proposed for the nonlinear Schrödinger equation. The methods are developed by applying the multiple relaxation idea to the exponential Runge-Kutta methods. It is shown that the multiple relaxation exponential Runge-Kutta methods can achieve high-order accuracy in time and preserve multiple original invariants at the discrete level. They are the first exponential-type methods that preserve multiple invariants. The number of invariants the methods preserve depends only on that of the relaxation parameters. Several numerical experiments are carried out to support the theoretical results and illustrate the effectiveness and efficiency of the proposed methods.

Speaker Introduction:

Li Dongfang, Professor and Ph.D. Supervisor at the School of Mathematics and Statistics, Huazhong University of Science and Technology, Huazhong Distinguished Scholar, and National High-level Young Talent. He has presided over 7 national-level projects. His research mainly focuses on numerical solutions of differential equations, machine learning, and signal processing. In particular, he has made significant progress in structure-preserving algorithms for differential equations and efficient numerical algorithms and theories for fractional differential equations.