摘  要：

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.

预备知识：

Differential equations, classical mechanics,exterior differential calculus

主讲人简介：

尚在久，中国科学院数学与系统科学研究院研究员、博士生导师，中国科学院大学岗位教师。曾任中国科学院数学与系统科学研究院数学研究所副所长（2003-2011）、所长（2012-2016）。 《中国科学：数学》（中、英文版）、 《数学学报》（中、英文版）、 《应用数学学报》（中、英文版）等期刊编委。从事动力系统及其几何数值方法的研究，曾获国家教委科技进步二等奖（1993），是“冯康等国家自然科学一等奖获奖项目“哈密尔顿系统的辛几何算法“（1997）的主要骨干成员，代表性成果有“辛算法的稳定性理论”、“保体积算法”等。