摘要
本文证明了 ,用差分法求解非线性发展方程的初值问题 ,当方程适定 ,在差分格式相容的条件下 ,稳定性等价于收敛性和逐点Lipschitz条件 .
The evolution equation is a system of partial difference eq ua tions, which has been widely applied in the dynamic mechanics theory and enginee ring. The difference method is adopted to solve the initial value problem of the nonlinear evolution equation in this paper. The solution stability is proved to be equivalent to the convergency and the point-by-point Lipschitz condition i f the equation is well posed and the difference pattern is compatible. As a resu lt, this leads to an extension of Lax theorem to the nonlinear case.
出处
《应用数学》
CSCD
北大核心
2002年第1期62-67,共6页
Mathematica Applicata
关键词
非线性发展方程
初值问题
差分法
Lax等价定理
稳定性
收敛性
差分格式
Initial value problem of the nonlinear evolution equation
D ifference method
Lax theorem
Stability
Convergency
Point-by-point Lipschit z condition
