求解Rosenau-RLW方程的一个线性化差分算法

A Linearized Difference Algorithm for Solving Rosenau-RLW Equation

摘要: 本文对一类带有齐次边界条件的Rosenau-RLW方程的初边值问题进行了数值研究，在保证二阶理论精度的前提下，对非线性项在时间层进行外推线性化处理，提出一个新的三层线性化差分格式，证明了差分解的存在唯一性，在不能得到差分解最大模先验估计的情况下，综合运用数学归纳法和离散泛函分析方法，证明了该差分格式的收敛性和稳定性。数值实验验证了该方法是可靠的。

Abstract: In this paper, the initial boundary value problem of a class of Rosenau-RLW equations with homogeneous boundary conditions is studied numerically. On the premise of ensuring the accuracy of the second order theory, the nonlinear terms are extrapolated into the time layer, and a new three-level linearized difference scheme is proposed, which proves the existence and uniqueness of the difference decomposition. In the absence of a priori estimate of the maximum modulus of difference decomposition, the convergence and stability of the difference scheme are proved by means of mathematical induction and discrete functional analysis. Numerical experiments show that the method is reliable.