论文标题
CAMASSA-HOLM方程的变分离散性数字研究
A numerical study of variational discretizations of the Camassa-Holm equation
论文作者
论文摘要
我们基于变化配方和能量保护，我们介绍了周期域中Camassa-Holm方程的两个半差异。第一个是真实行上现有保守的多eakon方法的定期版本，为此，我们提出了受Camassa和合作者作品启发的有效计算算法。第二种方法和主要感兴趣的方法是基于拉格朗日变量中的变异原理对两组分的Camassa-Holm系统进行新颖的离散化的周期性。应用显式ode求解器以及时集成，我们将各种离散化与几个数值示例的现有方法进行了比较。
We present two semidiscretizations of the Camassa-Holm equation in periodic domains based on variational formulations and energy conservation. The first is a periodic version of an existing conservative multipeakon method on the real line, for which we propose efficient computation algorithms inspired by works of Camassa and collaborators. The second method, and of primary interest, is the periodic counterpart of a novel discretization of a two-component Camassa-Holm system based on variational principles in Lagrangian variables. Applying explicit ODE solvers to integrate in time, we compare the variational discretizations to existing methods over several numerical examples.
