New quadrature rules for highly oscillatory integrals with stationary points
作者：
Highlights：
• A new framework for the numerical solution of highly oscillatory integrals is proposed.
• The integrals are bifurcated in the neighborhood of stationary point.
• The integral on the smaller subinterval is solved by hybrid functions and Haar wavelets.
• The integral on the longer subinterval is solved by the meshless method with MQ radial basis functions.
• Convergence analysis of the proposed methods is performed.
摘要
•A new framework for the numerical solution of highly oscillatory integrals is proposed.•The integrals are bifurcated in the neighborhood of stationary point.•The integral on the smaller subinterval is solved by hybrid functions and Haar wavelets.•The integral on the longer subinterval is solved by the meshless method with MQ radial basis functions.•Convergence analysis of the proposed methods is performed.
论文关键词：Oscillatory integrand,Quadrature,Critical point,Levin collocation method,Radial basis functions,Haar wavelets and hybrid functions
论文评审过程：Received 1 February 2014, Revised 14 June 2014, Available online 5 October 2014.
论文官网地址：https://doi.org/10.1016/j.cam.2014.09.019
