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Matrix numerical integration algorithms for rapidly oscillating functions

  • Numerical Methods for Solution of Equations
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Abstract

Efficient general quadrature formulas with nodes of arbitrary multiplicity are constructed for numerical integration of rapidly oscillating functions. The quadrature weights of these formulas are derived in explicit form in terms of easily evaluated integrals of products of a rapidly oscillating function and elementary basis functions and also in terms of elements of the inverse of the Vandermonde matrix. Error bounds are established for the quadrature formulas, which depend both on the integration increment and on the oscillation parameters. Necessary conditions are proved when the relative error is bounded and tends to zero with the increase of the oscillation parameters. Two-sided interpolation polynomials are applied to obtain easily computed posterior error bounds for quadrature formulas.

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References

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Authors
  1. A. F. Kalaida
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Additional information

Kiev University. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 75, pp. 12–20, 1991.

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Kalaida, A.F. Matrix numerical integration algorithms for rapidly oscillating functions. J Math Sci 72, 3053–3060 (1994). https://doi.org/10.1007/BF01259470

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  • DOI: https://doi.org/10.1007/BF01259470

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