Extrapolation Methods for Oscillatory Infinite Integrals
- 1 August 1980
- journal article
- Published by Oxford University Press (OUP) in IMA Journal of Applied Mathematics
- Vol. 26 (1) , 1-20
- https://doi.org/10.1093/imamat/26.1.1
Abstract
The non-linear transformations for accelerating the convergence of slowly convergent infinite integrals due to Levin & Sidi (1975) are modified in two ways. These modifications enable one to evaluate accurately some oscillatory infinite integrals with less work. Special emphasis is placed on the evaluation of Fourier and Hankel transforms and some simple algorithms for them are given. Convergence properties of these modifications are analysed in some detail and powerful convergence theorems are proved for certain cases including those of the Fourier and Hankel transforms treated here. Several numerical examples are also supplied.Keywords
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