求解广义Rosenau-Kawahara方程的一个非线性加权守恒差分格式  

A Nonlinear Weighted Conserved Difference Scheme for the Generalized Rosenau-Kawahara Equation

作　　者：张爽[1] 胡劲松 ZHANG Shuang;HU Jinsong(The Experimental School Affiliated to Xihua University,Chengdu 610039 China;School of Science,Xihua University,Chengdu 610039 China)

机构地区：[1]西华大学附属实验学校,四川成都610039 [2]西华大学理学院,四川成都610039

出　　处：《西华大学学报（自然科学版）》2024年第3期106-112,共7页Journal of Xihua University:Natural Science Edition

基　　金：四川省应用基础研究项目(2019JY0387)。

摘　　要：对广义Rosenau-Kawahara方程的初边值问题进行数值研究。在二阶精度前提下,在空间层引入两个加权系数,构造了一个带有两个加权系数的两层非线性差分格式。该格式很好地模拟了原问题的一个守恒性质。利用离散泛函分析方法证明了该格式的二阶收敛性与无条件稳定性。数值实验表明,通过适当调整两个加权系数可使计算精度大幅度提高,证明本文提出的加权格式是有效的。A numerical method for a class of generalized Rosenau-Kawahara equation with initial boundary value problem is studied.Based on the second order accuracy,a nonlinear two-level difference scheme is constructed when two weighted coefficients are introduced at the space level.The scheme can reasonably simulate the original conservation.By the discrete functional analysis method,the second order convergence and stability of the scheme are analyzed.Numerical experiments results show that the calculation accuracy can be greatly improved by adjusting the two weighting coefficients,which proves that the weighting scheme proposed in this paper is effective.

关 键 词：广义Rosenau-Kawahara方程 加权差分格式 守恒 收敛性 稳定性 

分 类 号：O241.82[理学—计算数学]