Local Truncation Error of Low-Order Fractional Variational Integrators
Local Truncation Error of Low-Order Fractional Variational Integrators
复制标题
低阶分数变分积分器的局部截断误差
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
S. Ober
中科院分区：
文献类型：
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作者：
F. Jiménez;S. Ober
本文研究了[1，2]中在Riewe和Cresson [3，4]工作的基础上发展起来的所谓分数阶变分积分器的局部截断误差。这些积分器是通过两个主要元素获得的：通过引入动力学曲线的分数阶导数来扩大通常的力学拉格朗日状态空间;以及离散约束变分原理，其精神在于离散力学和变分积分器[5]。分数阶变分积分器是为模拟分数阶耗散系统而设计的，在特殊情况下，分数阶耗散系统可归结为具有线性阻尼的机械系统。所有这些元素都在本文中介绍。此外，作为原始结果，我们证明了（第3节，定理2）分数阶变分积分器相对于线性阻尼力学系统动力学的局部截断误差的阶数。
We study the local truncation error of the so-called fractional variational integrators, recently developed in [1, 2] based on previous work by Riewe and Cresson [3, 4]. These integrators are obtained through two main elements: the enlarging of the usual mechanical Lagrangian state space by the introduction of the fractional derivatives of the dynamical curves; and a discrete restricted variational principle, in the spirit of discrete mechanics and variational integrators [5]. The fractional variational integrators are designed for modelling fractional dissipative systems, which, in particular cases, reduce to mechanical systems with linear damping. All these elements are introduced in the paper. In addition, as original result, we prove (Sect. 3, Theorem 2) the order of local truncation error of the fractional variational integrators with respect to the dynamics of mechanical systems with linear damping.
影响因子：
3
作者：
Jiménez F
通讯作者：
Jiménez F