Rosenau－Kawahara 方程的空间加权 C－N 差分格式

摘要

In this paper, a conservative Crank-Nicolson finite difference with weight coefficient is proposed by LAX scheme.The scheme has an advantage that it preserves some invariant properties of the original differential equation.It is shown that the finite difference scheme is convergent with second-order and unconditionally stable by discrete functional analysis method.Numerical experiment also shows that appropriate adjustments to the weighted parameter can significantly improve the computational accuracy.%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情况下，对空间层引入加权系数，提出1个两层非线性空间加权差分格式，格式合理地模拟了问题的2个守恒性质，得到差分解的先验估计，并利用离散泛函分析方法分析格式的收敛性与无条件稳定性。数值实验表明：该方法是可靠的，适当调整加权系数可以大幅提高计算精度。