%0 Journal Article
%T 代数和对数奇异Fourier积分的最速下降方法<br>The steepest descent method for Fourier integrals involving algebraic and logarithmic singular factors
%A 孔艺婷
%A 王同科&lt
%A br&gt
%A KONG Yi-ting
%A WANG Tong-ke
%J 山东大学学报（理学版）
%D 2017
%R 10.6040/j.issn.1671-9352.0.2016.558
%X 摘要： 针对有限和半无限区间上包含代数和对数奇异因子的振荡型Fourier积分,通过改变积分路径,将振荡因子变换为复平面上的快速衰减因子,使得积分不再振荡。对于转换后无穷区间上的奇异积分,可以使用修正的Gauss-Legendre求积方法高效计算,数值算例验证了理论分析的正确性和方法的高精度。<br>Abstract: For the oscillatory Fourier integral over finite or semi-infinite interval that has algebraic and logarithmic singularities at the endpoints, this paper converts the oscillatory factor to fast decaying factor by deforming the path of integration into complex plane such that the integral never oscillates along the new path. For the transformed singular integrals over semi-infinite interval, the modified Gauss-Legendre quadrature formula can be used to evaluate them efficiently. Numerical examples verify the correctness of the theoretical analysis and the high accuracy of the method
%K 有限或半无限区间
%K 振荡型Fourier积分
%K 代数和对数奇异
%K 最速下降方法
%K &lt
%K br&gt
%K oscillatory Fourier integral
%K the steepest descent method
%K finite or semi-infinite interval
%K algebraic and logarithmic singularity
%U http://lxbwk.njournal.sdu.edu.cn/CN/10.6040/j.issn.1671-9352.0.2016.558