Fractional variational integrators based on convolution quadrature
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910386315329536 |
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| author | Hariz, Khaled Jiménez, Fernando Ober-Blöbaum, Sina |
| author_facet | Hariz, Khaled Jiménez, Fernando Ober-Blöbaum, Sina |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_18362 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fractional variational integrators based on convolution quadrature Hariz, Khaled Jiménez, Fernando Ober-Blöbaum, Sina Numerical Analysis 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. |
| title | Fractional variational integrators based on convolution quadrature |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2403.18362 |