3维Helmholtz方程的4阶紧致有限差分格式  

Compact Fourth-Order Finite Difference Scheme for Three-Dimensional Helmholtz Equation

作　　者：曹莹[1] 孔令华[1] 王兰[1] 马院萍[1] 

机构地区：[1]江西师范大学数学与信息科学学院,江西南昌330022

出　　处：《江西师范大学学报（自然科学版）》2010年第6期597-599,共3页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：国家自然科学青年基金(10901074);江西省自然科学基金(2008GQS0054);江西省教育厅基金(GJJ09147);江西师范大学博士启动基金(2057)和青年成长基金(2390)以及研究生创新基金(YJS2010009)资助项目

摘　　要：对波数很大的3维Helmholtz方程提出了2个新的高阶紧致差分格式.格式主要优点是高精度且所用模板小.为此充分利用原方程构造出了2个4阶精度的格式,其中一个格式的截断误差主项与波数k有关,另一个无关.最后的数值结果和理论分析是互相一致的.Two new compact difference methods are discussed to solve the three dimensional Helmholtz equation with large wave numbers k.The main idea of the method is to solve the problem with high accuracy while with small stencils by the original equations.The proposed two compact schemes are fourth-order. The leading term of the truncation error of one method depends on the wave number k,and the other is independent.Numerical results suggest that the latter is a little more accurate than the former and both of them are fourth-order.

关 键 词：高阶紧格式 3维Helmholtz方程 截断误差 

分 类 号：O175.2[理学—数学]