2021/06/14 by Anil N. Hirani, Hirani, Anil N., Andy T. S. Wan +3
Mathematics · Physics and Astronomy · #37M05 #37M15 #65L05 #65L12 #65L20 #65L70 #65P10 #Dynamical Systems (math.DS) #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods for differential equations #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2106.07484
openalex publication_date 2021/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce conservative integrators for long term integration of piecewise smooth systems with transversal dynamics and piecewise smooth conserved quantities. In essence, for a piecewise dynamical system with piecewise defined conserved quantities such that its trajectories cross transversally to its interface, we combine Mannshardt's transition scheme and the Discrete Multiplier Method to obtain conservative integrators capable of preserving conserved quantities up to machine precision and accuracy order. We prove that the order of accuracy of the conservative integrators is preserved after crossing the interface in the case of codimension one number of conserved quantities. Numerical examples illustrate the preservation of accuracy order and conserved quantities across the interface.