论文标题
离散的变分方法和符号概括性添加剂runge-kutta方法
Discrete Variational Methods and Symplectic Generalized Additive Runge--Kutta Methods
论文作者
论文摘要
我们考虑一个拉格朗日系统$ l（q，\ dot q）= \ sum_ {l = 1}^{n} l^{\ {\ {l \}}（q，\ dot q）$，其中$ q $ -varia-variable由通用的添加剂runge-kutta（gark）方法处理。应用离散变化的技术，我们展示了如何构建符合性方案。假设给出的天然球的对角线方法，我们提出了一些用于构建过渡矩阵的技术。我们解决了方法的顺序问题，并讨论了一些半分离和可分离的问题，显示了一些具有非平方系数矩阵的方法的有趣构造。
We consider a Lagrangian system $L(q,\dot q) = \sum_{l=1}^{N}L^{\{l\}}(q,\dot q)$, where the $q$-variable is treated by a Generalized Additive Runge--Kutta (GARK) method. Applying the technique of discrete variations, we show how to construct symplectic schemes. Assuming the diagonal methods for the GARK given, we present some techinques for constructing the transition matrices. We address the problem of the order of the methods and discuss some semi-separable and separable problems, showing some interesting constructions of methods with non-square coefficient matrices.
