带混合阻尼边界的二维波动方程有限差分格式  

The finite difference scheme for two-dimensional wave equation with mixed damping boundary

作　　者：刘建康[1] 张珂 LIU Jian-kang;ZHANG Ke(School of Mathematical Science,Shanxi University,Taiyuan 030006,China)

机构地区：[1]山西大学数学科学学院,山西太原030006

出　　处：《陕西科技大学学报》2018年第2期167-174,共8页Journal of Shaanxi University of Science & Technology

基　　金：国家自然科学基金项目(91430109)

摘　　要：运用Taylor级数展开式,对左下边界为Robin边界,右上边界为Neumann阻尼边界的矩形域上的二维波动方程进行了离散,得到方程的三层全离散隐式有限差分格式,并利用离散能量方法构建了差分格式先验估计式,进而证明了所建差分格式在H2范数意义下关于时间和空间均二阶收敛,其结果对高维数值算法的研究具有重要理论意义,最后数值实验验证了理论结果.The discrete process is established for the wave equation by using Taylor expansion in rectangular domain with special conditions,where Robin boundary is on the upper left and Neumann damped boundary is on the low right.Then the three level implicit finite difference scheme for the wave equation is obtained.Prior estimation is constructed by discrete energy method.Further proof the difference scheme is convergent in H 2 norm,and the rate of convergence is of order 2.The results are of great theoretical significance to the study of high-dimensional numerical algorithms.The numerical experiments verify the theoretical results.

关 键 词：波动方程 有限差分 阻尼边界 收敛性 稳定性 

分 类 号：O241.82[理学—计算数学]