高振荡积分的复合中矩形公式外推算法  

Approximate Calculation of High Oscillatory Integrals

作　　者：于梦尧 王玲 龚佃选 张宇鑫 赵凯艳 李金 YU Meng-yao;WANG Ling;GONG Dian-xuan;ZHANG Yu-xin;ZHAO Kai-yan;LI Jin(College of Science,North China University of Science and Technology,Tangshan Hebei 063210,China)

机构地区：[1]华北理工大学理学院,河北唐山063210

出　　处：《华北理工大学学报（自然科学版）》2024年第4期128-136,共9页Journal of North China University of Science and Technology：Natural Science Edition

基　　金：河北省自然科学基金项目(A2019209533):典型区域上超奇异积分方程的高精度算法。

摘　　要：振荡积分在信号处理、波动等问题中有广泛的应用。本文利用复合中矩形公式近似计算高振荡积分,并根据求积公式推导出误差渐进展开式。然后在误差渐进展开式的基础上设计外推算法。并证明了外推算法的收敛阶及其收敛速度。最后,通过数值算例验证了算法的有效性。The oscillatory integral is widely applied in signal processing,wave propagation,and other related fields.Firstly,based on the composite midpoint rule,the high oscillatory integral was approximated,and the error asymptotic expansion was derived according to the integration formula.Then derives the asymptotic expansion of the error based on the integration formula.Nextly,based on the asymptotic expansion of the error,an extrapolation algorithm was designed.Furtherly,the convergence order and speed of the extrapolation algorithm were demonstrated.Finally,the effectiveness of the algorithm was verified through numerical examples.

关 键 词：振荡函数 复合中矩形 外推法 误差展开式 

分 类 号：O241.4[理学—计算数学]