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

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

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Article ID: iaor20122261
Volume: 236
Issue: 10
Start Page Number: 2696
End Page Number: 2705
Publication Date: Apr 2012
Journal: Journal of Computational and Applied Mathematics
Authors: , , ,
Keywords: integration
Abstract:

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.

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