An adaptive Filon-type method for oscillatory integrals without stationary points

作者：Zhao, Longbin; Huang, Chengming^*

来源：Numerical Algorithms, 2017, 75(3): 753-775.

DOI：10.1007/s11075-016-0219-3

• Oscillatory integral
• Filon-type method
• Asymptotic order

In this paper, we propose an adaptive Filon-type method to approximate oscillatory integrals. By using some S-shaped functions connecting Gauss-Legendre nodes and Filon-type method, the adaptive schemes behave well for small as well as for large frequencies. Adding frequency-dependent nodes can improve the asymptotic order at the same time. Moreover, there exist some complex nodes leading to a higher asymptotic order method approximating to the integral, and the special nodes work in other methods as well. The error can be further decreased by taking extra Chebyshev nodes. The efficiency and accuracy are tested by some experiments.

• 出版日期2017-7
• 单位华中科技大学