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A method for the integration of oscillatory functions

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Abstract

A method for the numerical evaluation of the integrals

$$I_1 (\lambda ) = \int_{ - 1}^1 {f(x)\sin (\lambda x)dx} andI_2 (\lambda ) = \int_{ - 1}^1 {f(x)\cos (\lambda x)dx} $$

is presented. The functionf(x) is approximated by a partial sum of its Legendre series.

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References

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  4. R. Piessens and F. Poleunis,A numerical method for the integration of oscillatory functions, BIT 11 (1971), 317–327.

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Authors and Affiliations

  1. School of Mathematics and Computing, the Polytechnic, Leeds, Yorkshire, England

    H. V. Smith

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  1. H. V. Smith
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Smith, H.V. A method for the integration of oscillatory functions. BIT 17, 338–343 (1977). https://doi.org/10.1007/BF01932154

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  • DOI: https://doi.org/10.1007/BF01932154

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