二维Helmholtz方程的高阶紧致差分方法  

High-Order Compact Difference Scheme for Solving Two-dimensional Helmholtz Equation

作　　者：葛永斌[1] 刘国涛[2] 

机构地区：[1]宁夏大学应用数学与力学研究所,银川750021 [2]航天科工集团第六研究院46所,呼和浩特010010

出　　处：《内蒙古大学学报（自然科学版）》2010年第2期176-180,共5页Journal of Inner Mongolia University：Natural Science Edition

基　　金：国家自然科学基金资助项目(10502026;10662006)

摘　　要：基于二阶导数的四阶Padé型紧致差分逼近式,并结合原方程本身,得到了二维Helm-holtz一种四阶精度的紧致差分格式.该格式在每个空间方向上只涉及到三个点处的未知量及其二阶导数值,边界处对于二阶导数利用四阶显式偏心格式.然后,利用Richardson外推法、算子插值法及二阶导数在边界点处的六阶显式偏心格式,将本文构造的二维Helmholtz方程四阶紧致差分格式的精度提高到六阶.最后,通过数值实验验证了本文方法的精确性和可靠性.Based on the Pade scheme of second-order derivatives, a fourth-order compact difference scheme is proposed for solving two-dimensional Helmhohz equation. Fourth-order explicit difference schemes are used to construct the same order discretization of boundary points. Then,the accuracy of the fourth-order compact difference schemes is upgraded to sixth-order by using Rich- ardson extrapolation technique and operator interpolation scheme. Sixth-order explicit difference schemes of second-order derivatives on the boundaries are used. At last, numerical experiments are given to prove the efficiency and dependability of present method.

关 键 词：HELMHOLTZ方程 高精度 紧致差分格式 RICHARDSON外推法 

分 类 号：O241.82[理学—计算数学]