广义Rosenau-KdV-RLW方程的一个新的高精度守恒差分格式  

A new high-accuracy conservative difference scheme for the generalized Rosenau-KdV-RLW equation

作　　者：胡俊林 刘哲含 胡劲松 HU Jun-lin;LIU Zhe-han;HU Jin-song(School of Science,Xihua University,Chengdu 610039,Sichuan,China)

机构地区：[1]西华大学理学院,四川成都610039

出　　处：《西北师范大学学报（自然科学版）》2024年第3期127-132,共6页Journal of Northwest Normal University(Natural Science)

基　　金：四川省应用基础研究资助项目(2019YJ0387);国家自然科学青年基金资助项目(11701481)。

摘　　要：对一类广义Rosenau-KdV-RLW方程的初边值问题提出一个新的高精度守恒差分算法.利用Taylor展式,在空间层做部分外推处理,直接从整体上抵消空间截断误差的二阶部分,在时间层采用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四阶精度;合理模拟了问题本身的一个守恒量,并利用离散Sobolev嵌入不等式和离散泛函分析方法,证明了格式的收敛性和稳定性;最后,数值算例验证了该方法的有效性.A new conservative difference algorithm with the high-accuracy is proposed for the initial boundary value problem of the generalized Rosenau-KdV-RLW equation.For the space direction in this scheme,the Taylor expansion and the partial extrapolation are used tOmake the second-order term of the truncation error be removed directly,then it can achieve the fourth-order accuracy.And for the time direction,the Crank-Nicolson method is performed sOthat it has second-order accuracy in time.This algorithm can simulate reasonably a conservative property of the original problem.By using discrete Sobolev embedding inequality and the discrete functional analysis method,the convergence and stability of this algorithm are proved,respectively.Finally,the numerical examples show that this algorithm is reliable.

关 键 词：广义Rosenau-KdV-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]