RLW方程的一个空间六阶精度非线性守恒差分格式  

A Nonlinear Conservative Difference Scheme for RLW Equation with Sixth Order Spatial Accuracy

作　　者：易莉佳 江跃勇 YI Lijia;JIANG Yueyong(School of Science,Xihua University,Chengdu,SiChuan 610039;College of Mathematics and Phyics,Mianyang Teachers'College,Mianyang,Sichuan 621000)

机构地区：[1]西华大学理学院,四川成都610039 [2]绵阳师范学院数理学院,四川绵阳621000

出　　处：《绵阳师范学院学报》2024年第5期16-22,37,共8页Journal of Mianyang Teachers＇ College

基　　金：国家自然科学基金项目(11701481);四川应用基础研究项目(2019JY0387)。

摘　　要：对RLW方程的一类初边值问题提出一个高精度守恒差分算法.利用Taylor展开,在空间层做Richardson外推组合的处理,时间层采用Crank-Nicolson格式,从而在时间方向和空间方向分别达到了二阶精度和六阶精度,并合理地模拟了问题本身的两个守恒量,证明了格式的收敛性和稳定性,数值算例也验证了该方法是有效的.In this paper,a high-precision conservative difference algorithm is proposed for a class of initial boundary value problems of the RLW equation.By using Taylor expansion and Richardson extrapolation combination in the spatial layer,and using the Crank-Nicholson scheme in the temporal layer,the second-order and sixth-order accuracy in the time and space directions were achieved,respectively.The two conserved quantities of the problem were reasonably simulated,and the convergence and stability of the scheme were proved.Numerical examples also verified the effectiveness of this method.

关 键 词：RLW方程 高精度 守恒 差分格式 收敛性 稳定性 

分 类 号：O241.82[理学—计算数学]