Is Symplectic-Energy-Momentum Integration Well-Posed?

2006/08/04 by Yosi Shibberu, Shibberu, Yosi
Computer Science · Engineering · Mathematics · #65L12 #70H05 #Electromagnetic Simulation and Numerical Methods #FOS: Physical sciences #Mathematical Physics (math-ph) #Modeling and Simulation Systems #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.math-ph/0608016

openalex publication_date 2006/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide new existence and uniqueness results for the discrete-time Hamilton (DTH) equations of a symplectic-energy-momentum (SEM) integrator. In particular, we identify points in extended-phase space where the DTH equations of SEM integration have no solution for arbitrarily small time steps. We use the nonlinear pendulum to illustrate the main ideas.

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