求解广义Rosenau-Kawahara-RLW方程的守恒差分算法

Conservative Difference Scheme for Solving General Rosenau-Kawahara-RLW Equation

对一类带有齐次边界条件的广义Rosenau-Kawahara-RLW方程进行了数值研究,提出了一个两层非线性有限差分格式,格式合理地模拟了问题的一个守恒性质,得到了差分解的先验估计和存在唯一性,并利用离散泛函分析方法分析了差分格式的二阶收敛性与无条件稳定性。

In this paper, the numerical solution of initial-boundary value problem for generalized Rosenau-Kawahara-RLW equation with non-homogeneous boundary is considered. A nonlinear two-level difference scheme is designed. The difference schemes can well simulate one conservative quantities of the problem. The priori existence and uniqueness of the finite difference solution are also obtained. It is proved that the finite difference scheme is convergent with second order and unconditional stable by discrete functional analysis method.