摘要
Korteweg-de Vries(KdV)方程是人们在研究一些物理问题时得到的非线性波 动方程,其解满足无穷多个守恒律．本文为该方程设计了一种差分格式,其采用的是有限 体积法．但与传统的有限体积法不同的是,它的数值解同时满足两个相关的守恒律．这样 可以更好地保持解的物理上的守恒性质．数值例子表明这一算法是有效的．
Korteweg-de Vries（KdV） equation is a nonlinear wave equation arising from physics study, whose solution satisfies infinitely many conservation laws. This paper designs a difference scheme for the equation, which is of the finite-volume type. Different from the traditional finite-volume schemes however, the scheme satisfies two related conservation laws of the equation. Designed in such a way, the scheme preserves better the physical conservation properties of the KdV equation. The numerical examples show the efficiency of the scheme.
出处
《应用数学与计算数学学报》
2005年第2期15-22,共8页
Communication on Applied Mathematics and Computation
关键词
KDV方程
守恒律
网格平均
函数重构
KdV equation, conservation laws, cell-average, reconstruction.
