Conservative Integrators for Piecewise Smooth Systems with Transversal Dynamics
Abstract
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.
Cite
@article{arxiv.2106.07484,
title = {Conservative Integrators for Piecewise Smooth Systems with Transversal Dynamics},
author = {Anil N. Hirani and Andy T. S. Wan and Nikolas Wojtalewicz},
journal= {arXiv preprint arXiv:2106.07484},
year = {2022}
}
Comments
Replaced Lemma 3.6 with an easier argument. Collected hypotheses of main theorem into the statement. Results unchanged. Added figures of conserved quantity error