Computational Mathematics: Dynamics, Geometry, and Algebra in Numerical Integration

Explore the intersection of computational dynamics, differential geometry, and combinatorial algebra in this 53-minute MUNI Seminar Series talk by Hans Munthe-Kaas. Delve into the evolution of numerical analysis, focusing on the importance of preserving geometric structures in simulations of dynamical systems. Learn about Geometric Numerical Integration and its significance in long-term simulations, where the quality of error becomes more crucial than its magnitude. Discover how this field has enriched computational engineering, with examples illustrating the interplay between dynamics, geometry, and algebra. Gain insights into topics such as Kepler's Solar System, the history of computers, vector spaces, symmetries, global analysis, object-oriented programming, finite element analysis, Euler's methods, symplectic integrators, and Taylor series. Suitable for scientists with a general background in computational engineering problems, this talk provides a comprehensive overview of recent advancements in structure-preserving discretization of differential equations.