This course is an introduction to geometric numerical integration for ordinary differential equations based on the theory of dynamical systems. The course will cover the following topics:
1) Brief introduction to basics of dynamical systems;
2) K. Feng’s idea on geometric numerical integration;
3) Symplectic integration methods for Hamiltonian systems;
4) Backward error theory of geometric integration methods;
5) Linear stability of symplectic methods;
6) Nonlinear stability of symplectic methods
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.