2021/09/25 by Elena Celledoni, Celledoni, Elena, Ergys Çokaj +7
Mathematics · Physics and Astronomy · #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2109.12325
openalex publication_date 2021/09/25 · openalex created_date 2022/11/30 · openalex updated_date 2026/07/28
Since their introduction, Lie group integrators have become a method of choice in many application areas. Various formulations of these integrators exist, and in this work we focus on Runge--Kutta--Munthe--Kaas methods. First, we briefly introduce this class of integrators, considering some of the practical aspects of their implementation, such as adaptive time stepping. We then present some mathematical background that allows us to apply them to some families of Lagrangian mechanical systems. We conclude with an application to a nontrivial mechanical system: the N-fold 3D pendulum.