北京雁栖湖应用数学研究院

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.