An improved algorithm for the evaluation of Cauchy principal value integrals of oscillatory functions and its application

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:280

Article

He, Guo¹  Xiang, Shuhuang¹ 

[1] Cent S Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China

关键词: Cauchy principal value;    Oscillatory integral;    Logarithmic singularity;    Chebyshev polynomial;    Clenshaw-Curtis points;   

DOI  :  10.1016/j.cam.2014.11.023

来源: Elsevier

【 摘 要 】

A new interpolatory-type quadrature rule is proposed for the numerical evaluation of Cauchy principal value integrals of oscillatory kind f(-1)(1) f(x)/x-te(iwx)dx, where tau is an element of (-1, 1). The method is based on an interpolatory procedure at Clenshaw-Curtis points and the singular point, and the fast computation of the modified moments with Cauchy type singularity. Based on this result, a new method is presented for the computation of the oscillatory integrals with logarithmic singularities too. These methods enjoy fast implementation and high accuracy. Convergence rates on omega are also provided. Numerical examples support the theoretical analyses. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free