广义Rosenau-Kawahara-RLW方程的一个非线性守恒差分逼近

A Conservative Nonlinear Difference Approximation of Generalized Rosenau-Kawahara-RLW Equation

对一类带有齐次边界条件的广义Rosenau-Kawahara-RLW方程进行数值研究,提出一个两层非线性有限差分格式,格式合理地模拟问题的2个守恒性质,得到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对差分格式的二阶收敛性与无条件稳定性进行了证明。

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