Some Thoughts on Methods for Evaluating a Class of Highly Oscillatory Integrals

P. J. Harris ()
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P. J. Harris: University of Brighton

A chapter in Integral Methods in Science and Engineering, 2011, pp 203-211 from Springer

Abstract: Abstract When using the boundary integral method for solving problems in acoustics it is necessary to evaluate integrals of the form $$\begin{array}{ll}{\displaystyle I = \int_{0}^{1} f(x) e^{ikg(x)} \: dx } & \mbox{1-D}\vspace{2mm}\\ {\displaystyle I = \int_{0}^{1} \int_{0}^{1}f(x,y) e^{ikg(x,y)} \: dx \: dy } \qquad & \mbox{2-D}\end{array}$$ where f and g are known functions and k is a known constant.

Keywords: Quadrature Rule; Quadrature Method; Quadrature Point; Oscillatory Integral; Piecewise Polynomial (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-8176-8238-5_19

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DOI: 10.1007/978-0-8176-8238-5_19

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