中文摘要：

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.

英文摘要：

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.