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

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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.

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

论文评审过程:Received 2 April 2010, Revised 7 October 2011, Available online 16 January 2012.

论文官网地址:https://doi.org/10.1016/j.cam.2012.01.007