求解广义Rosenau-KdV-RLW方程的守恒差分格式

本文对一类带有齐次边界条件的广义Rosenau-KdV-RLW方程的初边值问题进行了数值研究,提出了一个两层非线性Crank-Nicolson差分格式,格式合理地模拟了原问题的两个守恒性质.然后,本文证明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无条件稳定性.数值实验表明该方法是可靠的.

A conservation difference scheme for generalized Rosenau-KdV-RLW equation

In this paper, the numerical solution of initial-boundary value problem for generalized Rosenau-KdV-RLW equation with non-homogeneous boundary is considered. A nonlinear two-level Grank-Nicolson difference scheme is designed. The difference schemes simulate two conservative quantities of the problem well. The existence and uniqueness of the difference solutions are also proved. It is proved by the discrete energy method that the difference scheme is second-order convergence and unconditionally stable. Numerical experiments verify the theoretical results.