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

  • P. J. Harris

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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.University of BrightonBrightonUK

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