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

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Integral Methods in Science and Engineering

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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.

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References

  1. Harris, P.J., Chen, K.: An efficient method for evaluating the integral of a class of highly oscillatory functions. Journal of Comp. and App. Maths., 230, n. 2, 433–442 (2009).

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Authors and Affiliations

  1. University of Brighton, Brighton, UK

    P. J. Harris

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  1. P. J. Harris
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Correspondence to P. J. Harris .

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Editors and Affiliations

  1. , Department of Mathematical and Computer, The University of Tulsa, 800 South Tucker Drive, Tulsa, 74104-9700, USA

    Christian Constanda

  2. School of Computing, Engineering, and Ma, University of Brighton, Lewes Road, Brighton, BN2 4GJ, United Kingdom

    Paul J. Harris

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Harris, P.J. (2011). Some Thoughts on Methods for Evaluating a Class of Highly Oscillatory Integrals. In: Constanda, C., Harris, P. (eds) Integral Methods in Science and Engineering. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-8238-5_19

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