A well-conditioned Levin method for calculation of highly oscillatory integrals and its application

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:342

Article

Ma, Junjie¹ 

[1] Guizhou Univ, Sch Math & Stat, Guiyang 550025, Guizhou, Peoples R China

关键词: Spectral coefficient method;    Highly oscillatory integral;    Levin method;    Numerical integration;    Chebyshev polynomial;   

DOI  :  10.1016/j.cam.2018.03.044

来源: Elsevier

【 摘 要 】

This paper is devoted to studying efficient calculation of generalized Fourier transform integral(-1)xf(t)e(i omega g(t))dt. For the general phase function g(t), we develop a modified Levin method by the spectral coefficient approach. A sparse and well-conditioned linear system is constructed to help accelerate calculation of highly oscillatory integrals. Numerical examples are included to show the convergence properties of the new method with respect to both quantities of collocation points and the frequency omega. Furthermore, we apply this approach to solving oscillatory Volterra integral equations. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free