Geometric numerical methods for dynamical systems
Geometric numerical integration of dynamical systems or structure-preserving method for ordinary differential equations has become a vital area of numerical analysis since 1980’s. The key idea is that one should discretize a continuous system of differential equations with some geometric structure or physical invariant by preserving the structure or invariant properly, as Kang Feng proposed. The course introduces some basic geometric numerical methods including the symplectic method for Hamiltonian systems, the volume-preserving method for divergence-free systems, the contact method for contact systems and the Lie-group method for systems of differential equations defined on a Lie-group. We will also introduce some applications of the various structure-preserving methods to some typical problems.
Lecturer
Date
15th March ~ 26th July, 2022
Website
Prerequisite
Differential equations, classical mechanics,exterior differential calculus
Video Public
No
Notes Public
No
Lecturer Intro
Zaijiu Shang is a Professor of the Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and a Post Teacher at the University of Chinese Academy of Sciences (2015-). He was the deputy director (2003-2011) and the director (2012-2016) of the Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences. He has been served as a member of editorial boards of Acta Math. Appl. Sinica (2007-), Acta Math. Sinica (2009-), Science China: Mathematics (2013-), and Applied Mathematics (HUST 2013-). He is working in the fields of dynamical systems and geometrical numerical methods. He won the second prize in “the Science and Technology Progress Award of the State Education Commission (1993)”. He was one of the core members of the project “Symplectic Geometric Algorithms of Hamiltonian Systems” which won the first prize of the National Natural Science Awards (Kang Feng etc., 1997), and his representative achievements include stability theory of symplectic algorithms and volume-preserving algorithms for source-free systems.