Stability Analysis of Lie Group Integrators in Terms of Test Equations

EasyChair Preprint 13421

Abstract

Today, virtually any classical time integration method from system dynamics has its Lie group counterpart including implicit and (half-)explicit methods, methods for constrained and for unconstrained systems, variational integrators, one-step and multistep methods, Newmark type methods etc. There is not much known about the numerical stability of these methods in the application to stiff systems. More precisely, one would be interested in criteria and step size bounds that guarantee that the distance between two numerical solutions for different initial values remains bounded on infinite time intervals. In linear spaces, such error bounds are known, e.g., from the theory of B-stability for systems that satisfy a one-sided Lipschitz condition. In the present paper, we follow a different path and focus on the application of Lie group integrators to test problems from rigid body dynamics.

Keyphrases: Lie groups, Time integration, stability

@booklet{EasyChair:13421,
  author    = {Martin Arnold},
  title     = {Stability Analysis of Lie Group Integrators in Terms of Test Equations},
  howpublished = {EasyChair Preprint 13421},
  year      = {EasyChair, 2024}}