Rosenau-Kawahara方程的一个新的守恒差分算法

A New Conservative Difference Scheme for Rosenau-Kawahara Equation

对Rosenau-Kawahara方程的初边值问题进行了数值研究,提出一个三层线性加权差分格式,格式合理地模拟了问题的2个守恒性质,并利用离散泛函分析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:该方法是可靠的,且适当调整加权系数可以大幅提高计算精度。

In this paper, a finite difference method is presented for the initial value problems of Rosenau-Kawahara Equation.A three level linear conservation finite difference scheme with one weighted coefficient is designed.The scheme has the advantages that it preserves two invariant properties of the original differential equation.It is proved that the finite difference scheme is convergent with second-order and unconditionally stable by discrete functional analysis method.Numerical identification also shows that appropriate adjustments to the one weighted parameter will significantly improve the computational accuracy.