Rosenau-KdV-RLW方程的一个三层线性化差分方法

A three-level linearized difference scheme for Rosenau-KdV-RLW equation

摘要:

本文对带有齐次边界条件的Rosenau-KdV-RLW方程的初边值问题进行了数值研究，提出了一个具有二阶理论精度的三层线性化差分格式，证明了差分解的存在唯一性. 尽管无法得到差分解的最大模估计，本文仍然综合运用数学归纳法和离散泛函分析方法证明了该格式的收敛性和稳定性.数值实验表明该方法是可靠的.

Abstract:

In this paper, numerical solution of the initial-boundary value problem for the Rosenau-KdV-RLW equation under homogeneous boundary is considered. A three-level linear difference scheme with second order accuracy is proposed and the existence and uniqueness of the difference solution are proved. Despite the absence of the maximum mold estimation of the difference solutions, we still prove that the difference scheme is convergent and stable by using the mathematical induction and discrete function analysis. The analytical results are demonstrated by the numerical examples.