延拓配置变分积分器
Prolongation-Collocation Variational Integrators
AI总结：
提出一种基于Hermite插值和Euler-Maclaurin求积公式的延拓配置技术，用于构造哈密顿系统的高阶变分积分器，并分析其阶数精度。
摘要：
我们引入了一种新技术，用于构造哈密顿常微分方程组的高阶变分积分器。具体而言，我们关注生成哈密顿系统解的全局光滑近似。离散拉格朗日量的构造采用Hermite插值多项式和Euler-Maclaurin求积公式，并涉及对Euler-Lagrange方程及其延拓应用配置方法。我们重点分析了所得变分积分器的阶数，这取决于Hermite多项式的逼近性质和求积误差。最后，对这些积分器中的一部分进行了性能比较。
英文摘要：
We introduce a novel technique for constructing higher-order variational integrators for Hamiltonian systems of ODEs. In particular, we are concerned with generating globally smooth approximations to solutions of a Hamiltonian system. Our construction of the discrete Lagrangian adopts Hermite interpolation polynomials and the Euler-Maclaurin quadrature formula, and involves applying collocation to the Euler-Lagrange equation and its prolongation. Considerable attention is devoted to the order analysis of the resulting variational integrators in terms of approximation properties of the Hermite polynomials and quadrature errors. A performance comparison is presented on a selection of these integrators.
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