Fractional variational integrators based on convolution quadrature
Abstract
Fractional dissipation is a powerful tool to study non-local physical phenomena such as damping models. The design of geometric, in particular, variational integrators for the numerical simulation of such systems relies on a variational formulation of the model. In [19], a new approach is proposed to deal with dissipative systems including fractionally damped systems in a variational way for both, the continuous and discrete setting. It is based on the doubling of variables and their fractional derivatives. The aim of this work is to derive higher-order fractional variational integrators by means of convolution quadrature (CQ) based on backward difference formulas. We then provide numerical methods that are of order 2 improving a previous result in [19]. The convergence properties of the fractional variational integrators and saturation effects due to the approximation of the fractional derivatives by CQ are studied numerically.
Cite
@article{arxiv.2403.18362,
title = {Fractional variational integrators based on convolution quadrature},
author = {Khaled Hariz and Fernando Jiménez and Sina Ober-Blöbaum},
journal= {arXiv preprint arXiv:2403.18362},
year = {2024}
}