Analysis of a collocation method for integrating rapidly oscillatory functions

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Abstract

A collocation method for approximating integrals of rapidly oscillatory functions is analyzed. The method is efficient for integrals involving Bessel functions Jv(rx) with a large oscillation frequency parameter r, as well as for many other one-and multi-dimensional integrals of functions with rapid irregular oscillations. The analysis provides a convergence rate and it shows that the relative error of the method is even decreasing as the frequency of the oscillations increases.

Original languageEnglish
Pages (from-to)131-138
Number of pages8
JournalJournal of Computational and Applied Mathematics
Volume78
Issue number1
DOIs
StatePublished - 3 Feb 1997

Keywords

  • Collocation analysis
  • Oscillatory integrals

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