Abstract
Kang Feng proposed the symplectic geometric algorithms for Hamiltonian systems at Beijing “International Symposium on Differential Geometry and Differential Equations” in August 1984, opening up a new field of research. Over the past 40 years, geometric numerical integration for dynamical systems has been irreplaceably applied in numerous fields, including celestial mechanics, plasma physics, fluid mechanics, biochemistry, meteorological forecasting, seismic exploration, data science and artificial intelligence. This paper mainly summarizes the achievements of geometric numerical integration for dynamical systems in China over the past 40 years.
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