Fractional variational integrators based on convolution quadrature
CoRR(2024)
摘要
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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