论文标题
线性和非线性波方程的不变保护法律的离散
Invariant Conservation Law-Preserving Discretizations of Linear and Nonlinear Wave Equations
论文作者
论文摘要
使用差异方程的谎言点对称性以及离散的直接乘数保护法构建方法的谎言点对称性，可以在五分和九点模板上获得对称和保护法律的有限差异化离散化。特别是，对于线性波方程，提出了一个显式的五点方案，以保留其基本几何点对称性的离散类似物和六个相应的保护定律。对于在超弹性中产生的一类非线性波方程，构建了九点隐式方案，保留了四个点对称性和三个局部保护定律。讨论了保留不同保护法的非线性波方程的其他离散化。
Symmetry- and conservation law-preserving finite difference discretizations are obtained for linear and nonlinear one-dimensional wave equations on five- and nine-point stencils, using the theory of Lie point symmetries of difference equations, and the discrete direct multiplier method of conservation law construction. In particular, for the linear wave equation, an explicit five-point scheme is presented that preserves the discrete analogs of its basic geometric point symmetries, and six of the corresponding conservation laws. For a class of nonlinear wave equations arising in hyperelasticity, a nine-point implicit scheme is constructed, preserving four point symmetries and three local conservation laws. Other discretization of the nonlinear wave equations preserving different subsets of conservation laws are discussed.
