求解BBM方程的一个新的高精度线性化差分算法  

A new high accuracy linearized difference algorithm for the BBM equation

作　　者：沙婵娟 张虹 SHA Chan-Juan;ZHANG Hong(School of Mathematical Sciences,Shanxi University,Taiyuan 030006,China;Hope College,Southwest Jiaotong University,Chengdu 610400,China)

机构地区：[1]山西大学数学科学学院,太原030006 [2]西南交通大学希望学院,成都610400

出　　处：《四川大学学报（自然科学版）》2021年第1期31-36,共6页Journal of Sichuan University(Natural Science Edition)

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

摘　　要：本文对一类带有齐次边界条件的Benjamin-Bona-Mahony方程的初边值问题进行了数值研究.通过先在时间层外推对问题进行线性化离散处理,然后再利用Richardson外推的思想在空间层进行外推,本文提出了一个理论精度为O(τ^2+h^4)的三层线性差分格式,证明了差分解的存在唯一性.在不能得到问题差分解的最大模估计的情况下,本文综合运用数学归纳法和离散泛函分析方法直接证明了该差分格式的收敛性和稳定性.数值实验表明该格式的精度明显优于已有的线性层差分格式.In this paper,an initial boundary value problem of Benjamin-Bona-Mahony equation is studied numerically.Firstly,the problem is discretized and linearized by extrapolating in time layer,and then extrapolated at the space level with Richardson's extrapolation idea,thus a three-layer linear difference scheme with O(τ^2+h^4)theoretical accuracy is proposed.Secondly,the existence and uniqueness of the discrete solution are proved.Finally,the convergence and stability of the scheme are proved by combining mathematical induction and discrete functional analysis.Numerical experiments show that the accuracy of the scheme is obviously better than the known linear layer difference scheme.

关 键 词：Benjamin-Bona-Mahony方程 线性差分格式 收敛性 稳定性 

分 类 号：O241.82[理学—计算数学]