Rosenau-Kawahara方程的一种空间加权线性守恒差分算法

A Weighted Linear Conservative Finite Difference Scheme for Rosenau-Kawahara Equation

对Rosenau-Kawahara方程的初边值问题进行数值研究,利用LAX加权差分格式的构造思想,在保持二阶理论精度的前提下,对空间层引入加权系数θ,提出了一个空间加权线性差分格式。格式合理地模拟了问题的2个守恒性质,证明了差分解的存在唯一性,并利用能量方法分析了格式的二阶收敛性与无条件稳定性。数值实验表明,通过适当地调整选择加权系数θ,可将计算精度显著提高。

In this paper, a linear conservation finite difference scheme with one weighted coefficient is designed by LAX scheme. The scheme has the advantages that it preserves some invariant properties of the original differential equation. It simulated the conservation properties of the problem well. The prior estimate, existence and uniqueness of the finite difference solution were also obtained. It was proved that the finite difference scheme is convergent with second - order and unconditionally stable by energy method. Numerical experiment result shows that appropriate adjustments to the weighted parameters would significantly improve the computational accuracy