2017/02/27 by Ander Murua, Murua, A., J. M. Sanz‐Serna +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Waves and Solitons #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1702.08354
openalex publication_date 2017/02/27 · openalex created_date 2017/03/16 · openalex updated_date 2026/07/28
In a series of papers the present authors and their coworkers have developed a family of algebraic techniques to solve a number of problems in the theory of discrete or continuous dynamical systems and to analyze numerical integrators. Given a specific problem, those techniques construct an abstract, \em universal version of it which is solved algebraically; then, the results are tranferred to the original problem with the help of a suitable morphism. In earlier contributions, the abstract problem is formulated either in the dual of the shuffle Hopf algebra or in the dual of the Connes-Kreimer Hopf algebra. In the present contribution we extend these techniques to more general Hopf algebras, which in some cases lead to more efficient computations.