摘要
奇异积分方程的快速求解都需要准确计算奇异积分,所以研究复合矩形求积公式近似计算柯西主值积分具有实际应用价值。在积分的计算中,逼近密度函数与核函数,得到误差渐近展开式,构造序列来逼近奇异点,在此基础上,设计外推算法提高计算精度,并证明了外推法的收敛速度。结果表明:数值结果验证了算法的有效性和理论分析的正确性。
The solution of singular integral equations requires to calculate singular integrals accurately.Therefore,it is of practical value to study the approximate calculation of Cauchy principal value integral by composite rectangle formula.In the calculation of singular integral,the error asymptotic expansion was obtained by approximating the density function and kernel function.Asequence was constructed to approximate singular points.On this basis,the extrapolation algorithm was used to improve the calculation accuracy and the convergence speed of the extrapolation method was proved.The results show that some numerical examples are given to verify the effectiveness of the algorithm and the correctness of the theoretical analysis.
作者
李金
张晓蕾
桑瑜
张宇鑫
LI Jin;ZHANG Xiao-lei;SANG Yu;ZHANG Yu-xin(College of Science,North China University of Science and Technology,Tangshan Hebei 063210,China)
出处
《华北理工大学学报（自然科学版）》
CAS
2022年第2期80-91,105,共13页
Journal of North China University of Science and Technology：Natural Science Edition
基金
国家自然科学基金项目(11771398)
河北省自然科学基金项目(A2019209533)。
关键词
柯西主值积分
外推法
复合矩形公式
误差展开式
Cauchy principal value integral
extrapolation method
composite rectangle formula
error expansion
