A rapid solution of a kind of 1D Fredholm oscillatory integral equation

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:236

Article

Li, Jianbing¹  Wang, Xuesong¹  Xiao, Shunping¹  Wang, Tao¹ 

[1] Natl Univ Def Technol, Coll Elect Sci & Engn, Changsha 410073, Hunan, Peoples R China

关键词: Oscillatory integral equation;    Levin method;    Spectral method;    Chebyshev differentiation matrix;    Stationary phase point;    Barycentric interpolation;   

DOI  :  10.1016/j.cam.2012.01.007

来源: Elsevier

【 摘 要 】

How to solve oscillatory integral equations rapidly and accurately is an issue that attracts special attention in many engineering fields and theoretical studies. In this paper, a rapid solution method is put forward to solve a kind of special oscillatory integral equation whose unknown function is much less oscillatory than the kernel function. In the method, an improved-Levin quadrature method is adopted to solve the oscillatory integrals. On the one hand, the employment of this quadrature method makes the proposed method very accurate; on the other hand, only a small number of small-scaled systems of linear equations are required to be solved, so the computational complexity is also very small. Numerical examples confirm the advantages of the method. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free