求解BBM方程的高精度非线性CN差分格式

High precise nonlinear CN difference scheme for BBM Equation

摘要:

本文对一类带有齐次边界条件的BBM方程的初边值问题进行了数值研究，提出了一个在时间上具有二阶理论精度，在空间上具有四阶理论精度的两层非线性Crank-Nicolson差分格式，该格式合理地模拟了原问题的一个守恒性质.此外，本文还讨论了差分解的存在唯一性，并利用能量方法分析了该格式的二阶收敛性与稳定性. 数值实验表明该方法是可靠的.

Abstract:

In this paper, numerical solution for the initial-boundary value problem of BBM equation with homogeneous boundary is considered. A two-level nonlinear difference scheme with second order in time and fourth order in space is proposed. The difference scheme simulates the conservation property of the problem. The existence and uniqueness of the difference solutions are proved. Using the discrete energy method, the stability and convergence are proved. Numerical experiments confirm the theortical results.