阻尼板振动方程的紧致差分方法  

A COMPACT DIFFERENCE METHOD FOR DAMPED PLATE VIBRATION EQUATION

作　　者：吴彩莲 朱爱玲 Wu Cailian;Zhu Ailing(School of Mathematics and Statistics,Shandong Normal University,Jinan 250358)

机构地区：[1]山东师范大学数学与统计学院,济南250358

出　　处：《高等学校计算数学学报》2023年第2期144-163,共20页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金资助项目(12171287);山东省自然科学基金资助项目(ZR2021MA063)。

摘　　要：1引言考虑如下阻尼板振动方程初边值问题■其中?=(0,a)×(0,b)?R2,T是时间总量,■μ(μ>0)为阻尼系数,ρ为给定正常数,f(x,y,t)是已知函数,φ1(x,y)和φ2(x,y)是初值函数,ψ1(y,t),ψ2(y,t),ψ3(x,t),ψ4(x,t)和g1(y,t),g2(y,t),g3(x,t),g4(x,t)是边值函数.In this paper,the fourth-order damped plate vibration equation is transformed into system of two second-order differential equations by introducing an intermediate variable.A four-order compact difference scheme for the initialboundary value problem of the damped plate vibration equation is established,which the compact difference method is used.Then the stability and convergence of the difference scheme is analyzed by the Fourier method,and the convergence is analyzed by the energy method.It proves that the error of the scheme is O(τ~2+h~4).Finally,some numerical calculation examples are given.The results of the calculation examples verify the accuracy and validity of the scheme.

关 键 词：振动方程 初边值问题 阻尼板 阻尼系数 已知函数 值函数 紧致差分方法 

分 类 号：O241.82[理学—计算数学]