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: | Wang Tao, Li Jianbing, Wang Xuesong, Xiao Shunping |
Keywords: | integration |
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.