Rosenau-Burgers方程的一种高精度有限差分格式  

A high-order accuracy finite difference scheme for the Rosenau-Burgers equation

作　　者：罗诗栋 凌永辉 LUO Shidong;LING Yonghui(School of Mathematics and Statistics,Minnan Normal University,Zhangzhou,Fujian 363000,China)

机构地区：[1]闽南师范大学数学与统计学院,福建漳州363000

出　　处：《闽南师范大学学报（自然科学版）》2022年第4期5-12,共8页Journal of Minnan Normal University：Natural Science

基　　金：福建省自然科学基金面上项目(2022J01896);福建省高校杰出青年科研人才培育计划项目。

摘　　要：针对Rosenau-Burgers方程提出一种保能量耗散性的三层线性隐式高精度差分格式,在时间和空间上分别达到二阶和四阶精度.使用离散能量法证明了差分格式数值解的存在性、有界性和收敛性,数值算例验证了该格式的有效性.Athree-level linear implicit finite difference scheme with energy dissipation for solving the Rosenau-Burgers equation is proposed.This scheme has second-order and fourth-order in time and space,respectively.The existence and boundedness of numerical solutions for the scheme are discussed.In addiction,the convergence of the numerical solution is proved by using the discrete energy technique.Numerical examples show that the proposed scheme is efficient.

关 键 词：Rosenau-Burgers方程 有限差分格式 收敛性 高精度 

分 类 号：O241.82[理学—计算数学]