Lorenz方程组的有限差分格式的长时间行为

摘要

The Lorenz equations possessing a global attractor are considered, the backward Euler scheme and the Crank-Nicolson scheme for the Lorenz equations is constructed. The dynamical properties of the discrete dynamical systems which are generated by the backward Euler scheme and the Crank-Nicolson scheme are analyzed, the existence of global attractor for the discrete dynamical systems is proved, the stability and the convergence of the finite difference schemes over a finite time interval (0, T] are obtained.%考虑带有整体吸引子的Lorenz方程组,研究由Euler隐格式和一类Crank-Nicolson格式生成的离散动力系统,证明这些离散动力系统都存在整体的吸引子.同时证明两个差分格式在有限的时间段[0,T]上的稳定性和差分解的收敛性.