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


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.


Quadrature Rule Quadrature Method Quadrature Point Oscillatory Integral Piecewise Polynomial 


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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.University of BrightonBrightonUK

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