A well-conditioned Levin method for calculation of highly oscillatory integrals and its application
A well-conditioned Levin method for calculation of highly oscillatory integrals and its application
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DOI：
10.1016/j.cam.2018.03.044
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发表时间：
2018-11-01
影响因子：
2.4
通讯作者：
Liu, Huilan
中科院分区：
文献类型：
--
作者：
Ma, Junjie;Liu, Huilan
本文致力于研究广义傅立叶变换积分(-1)xf(t)e(i omega g(t))dt的高效计算。对于一般相位函数 g(t)，我们通过谱系数方法开发了一种改进的 Levin 方法。构建了稀疏且条件良好的线性系统，以帮助加速高振荡积分的计算。数值例子显示了新方法在配置点数量和频率欧米伽方面的收敛特性。此外，我们应用这种方法来求解振荡 Volterra 积分方程。 (C) 2018 Elsevier B.V. 保留所有权利。
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.