求解波动方程的2种显式高精度紧致差分格式  

Two Kinds of Explicit High Order Compact Difference Schemes for Solving Wave Equations

作　　者：姜蕴芝 葛永斌[1] 

机构地区：[1]宁夏大学数学统计学院,宁夏银川750021

出　　处：《四川师范大学学报（自然科学版）》2017年第2期177-183,共7页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11361045)

摘　　要：针对一维波动方程,空间采用四阶Padé逼近,时间采用中心差分离散得到了一种时间二阶、空间四阶精度的显式紧致差分格式,其截断误差为O(τ~2+h^4).之后采用截断误差余项修正的方法对时间离散进行改进,改进后的格式的截断误差为O(τ~4+τ~2h^2+h^4),即格式具有整体四阶精度.然后,通过Fourier方法分析了2种格式的稳定性.最后,通过数值实验验证了本格式的精确性和可靠性.In this paper,an explicit compact difference scheme is obtained for solving the one dimensional wave equation. The truncation error of the scheme is O（ τ^2＋ h^4）. It＇s constructed by applying the fourth-order accurate Padé approximation in space and the second-order accurate central difference in time. Then,the remainder of the truncation error correction method is employed to improve the accuracy of the discretization of time,the truncation error of the improved scheme is O（ τ^4＋ τ^2h^2＋ h^4）,which means the scheme has an overall fourth-order accuracy. And then,the stability conditions of the two schemes are obtained by the Fourier method.Finally,the accuracy and the reliability of the present two schemes are verified by numerical experiments.

关 键 词：波动方程 PADÉ逼近 紧致格式 显式差分 稳定性 

分 类 号：O242.1[理学—计算数学]