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arXiv · 2403.18362

Fractional variational integrators based on convolution quadrature

Khaled Hariz·Fernando Jiménez·Sina Ober-Blöbaum
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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.

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Khaled Hariz, Fernando Jiménez, Sina Ober-Blöbaum. 2024-03-27. Fractional variational integrators based on convolution quadrature. https://arxiv.org/abs/2403.18362

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