Kuramoto-Sivashinsky方程的线性化L∞-差分方法  

A Linearized L∞-finite Difference Method for the Kuramoto-Sivashinsky Equation

作　　者：李娟[1] LI Juan(Department of Basic Course,Nanjing Audit University Jinshen College,Nanjing 210023,China)

机构地区：[1]南京审计大学金审学院基础部,江苏南京210023

出　　处：《数学的实践与认识》2020年第9期210-222,共13页Mathematics in Practice and Theory

基　　金：江苏省高校自然科学研究面上项目资助(16KJD110002);江苏省高等教育教学改革资助项目(2017JSJG541);江苏省高校‘青蓝工程’资助项目。

摘　　要：利用有限差分方法研究Kuramoto-Sivashinsky方程初边值问题的数值解.首先,给出了二阶线性化隐式差分格式,该格式在每一时间层均为线性方程组.其次,给出差分格式的守恒性和数值解的有界性.第三,证明差分格式在最大模意义下的收敛性.最后,通过数值算例验证差分格式的收敛阶,并数值模拟方程的混沌解.A linearized finite difference method is applied to the initial boundary value problem of Kuramoto-Sivashinsky equation.Firstly,a second order linearized implicit difference scheme is presented.The numerical scheme is a system of linear equations at each time level.Secondly,conservation of difference scheme and boundedness of numerical solutions are given.Thirdly,the convergence of difference scheme is proved in the sense of maximum modulus.Finally,the convergence order of the difference scheme is verified by numerical examples.The chaotic instability of the solution of the equation is numerically simulated.

关 键 词：KURAMOTO-SIVASHINSKY方程 线性化差分格式 收敛性 非线性问题 线性化 

分 类 号：O241.3[理学—计算数学]