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Numerical approximation of vector-valued highly oscillatory integrals

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Abstract

We present a method for the efficient approximation of integrals with highly oscillatory vector-valued kernels, such as integrals involving Airy functions or Bessel functions. We construct a vector-valued version of the asymptotic expansion, which allows us to determine the asymptotic order of a Levin-type method. Levin-type methods are constructed using collocation, and choosing a basis based on the asymptotic expansion results in an approximation with significantly higher asymptotic order.

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Authors and Affiliations

  1. Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Rd, Cambridge, CB3 0WA, UK

    S. Olver

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  1. S. Olver
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Correspondence to S. Olver.

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AMS subject classification (2000)

65D30

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Olver, S. Numerical approximation of vector-valued highly oscillatory integrals . Bit Numer Math 47, 637–655 (2007). https://doi.org/10.1007/s10543-007-0137-9

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  • DOI: https://doi.org/10.1007/s10543-007-0137-9

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