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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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A user-friendly extrapolation method for oscillatory infinite integrals
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by Avram Sidi PDF
Math. Comp. 51 (1988), 249-266 Request permission

Abstract:

In a recent publication [4] the author developed an extrapolation method, the W-transformation, for the accurate computation of convergent oscillatory infinite integrals. In yet another publication [6] this method was shown to be applicable to divergent oscillatory infinite integrals that are defined in the sense of summability. The application of the W-transformation involves some asymptotic analysis of the integrand as the variable of integration tends to infinity. In the present work the W-transformation is modified so as to keep this asymptotic analysis to a minimum, involving only the phase of oscillations. This modified version, which turns out to be as efficient as the original W-transformation, can also be applied to convergent or divergent oscillatory infinite integrals other than those dealt with in [4] and [6]. The convergence properties of the modified transformation are analyzed in detail for the integrals of [4] and [6], and numerical examples are provided.
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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Math. Comp. 51 (1988), 249-266
  • MSC: Primary 65D30; Secondary 41A55, 65B05
  • DOI: https://doi.org/10.1090/S0025-5718-1988-0942153-5
  • MathSciNet review: 942153