一维Helmholtz方程的四阶紧致有限体积方法  

FOURTH-ORDER COMPACT FINITE VOLUME SCHEMES FOR 1D HELMHOLTZ EQUATION

作　　者：孙晓峰[1] 姜子文[1] 

机构地区：[1]山东师范大学数学科学学院,济南250014

出　　处：《山东师范大学学报（自然科学版）》2016年第4期7-11,共5页Journal of Shandong Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11171193);山东省科技发展计划资助项目(2012GGB01198);山东省自然科学基金资助项目(ZR2014AM033)

摘　　要：本文分别提出了一维Helmholtz方程基于Dirichlet和周期边值问题的四阶紧致有限体积方法.对于Dirichlet边值问题,通过Taylor展开给出了方程的四阶紧致有限体积格式,并结合边界处的四阶近似,证明了此问题的离散格式是四阶格式.对于周期边值问题,利用周期边界条件,同样得到了此问题的四阶紧致有限体积格式.数值实验表明给出的两种格式均是四阶格式.In this paper, we propose fourth-order compact finite volume methods for the one-dimensional Helmholtz equation with the Dirichlet and periodic boundary conditions. For the former, we give the fourth-order compact finite volume scheme of the equation by Taylor expansion, and prove that the discrete scheme of the problem is fourth-order scheme combined with the fourth-order approximation of the boundary.For the latter, the fourth-order compact finite volume scheme is obtained using the periodic boundary condition.Numerical experiments show that the present schemes are fourth-order schemes for solving the one-Dimensional Helmholtz equation.

关 键 词：HELMHOLTZ方程 紧致有限体积方法 截断误差 

分 类 号：O241[理学—计算数学]