论文标题
保存保护法的新技术
A new technique for preserving conservation laws
论文作者
论文摘要
本文介绍了一种新的符号数字策略，以查找保留多个局部保护定律的给定PDE的半零食。我们证明，对于一个空间维度，文献中的各种一步时间集成商保留了完全离散的地方保护法，其密度是二次或哈密顿量。该方法将其他类型的步骤和保护定律推广到时代集成商；可以通过迭代新策略来治疗高维的PDE。我们将BousSinesQ方程式用作基准，并介绍了保留三个保护法律的第二和第四订单方案的新家庭。我们表明，对于具有三个因变量的PDE，新技术是可行的，作为一个潜在的Kadomtsev-PetviaShvili方程的二阶方案的新家族的示例。
This paper introduces a new symbolic-numeric strategy for finding semidiscretizations of a given PDE that preserve multiple local conservation laws. We prove that for one spatial dimension, various one-step time integrators from the literature preserve fully discrete local conservation laws whose densities are either quadratic or a Hamiltonian. The approach generalizes to time integrators with more steps and conservation laws of other kinds; higher-dimensional PDEs can be treated by iterating the new strategy. We use the Boussinesq equation as a benchmark and introduce new families of schemes of order two and four that preserve three conservation laws. We show that the new technique is practicable for PDEs with three dependent variables, introducing as an example new families of second-order schemes for the potential Kadomtsev-Petviashvili equation.
