Norges Teknisk-naturvitenskapelige Universitet Efficient Quadrature of Highly Oscillatory Integrals Using Derivatives Efficient Quadrature of Highly Oscillatory Integrals Using Derivatives
Norges Teknisk-naturvitenskapelige Universitet Efficient Quadrature of Highly Oscillatory Integrals Using Derivatives Efficient Quadrature of Highly Oscillatory Integrals Using Derivatives
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影响因子：
3.1
通讯作者：
A. Iserles;S. P. Nørsett
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作者：
A. Iserles;S. P. Nørsett
本文探讨了高振荡积分的求积分方法。推广平稳相位法，将这类积分展开为频率反幂的渐近级数。结果是两种方法，一种基于渐近级数的截断，另一种扩展了Filon工作中隐含的方法。这两种方法都将积分近似为函数值和导数的线性组合，其系数可能取决于频率。我们确定了这些方法的渐近性质，证明了它们的性能随着频率的增加而急剧提高，这可能与直觉相反。论文附有数值结果，证明了这套思想的潜力。
In this paper we explore quadrature methods for highly oscillatory integrals. Generalizing the method of stationary phase, we expand such integrals into asymptotic series in inverse powers of the frequency. The outcome are two families of methods , one based on a truncation of the asymptotic series and the other extending an approach implicit in the work of Filon. Both kinds of methods approximate the integral as a linear combination of function values and derivatives, with coefficients that may depend on frequency. We determine asymptotic properties of these methods, proving that, perhaps counterintuitively, their performance drastically improves as frequency grows. The paper is accompanied by numerical results that demonstrate the potential of this set of ideas.