A case of asymptotic summation in a two-dimensional domain

ASYMPTOTIC expressions are obtained for double sums with rapidly oscillating summands, suitable in the case of a sufficiently slow variation of the amplitude and phase increments of he summands over the range of summation. A very general type of computational algorithm is obtained by applying a Pois...

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Bibliographic Details
Published in:U.S.S.R. computational mathematics and mathematical physics 1978, Vol.18 (3), p.24-33
Main Authors: Karatygin, V.A., Rozov, V.A., Sokolova, N.O.
Format: Article
Language:English
Online Access:Get full text
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Summary:ASYMPTOTIC expressions are obtained for double sums with rapidly oscillating summands, suitable in the case of a sufficiently slow variation of the amplitude and phase increments of he summands over the range of summation. A very general type of computational algorithm is obtained by applying a Poisson transformation for the multiple sums, followed by application of the stationary phase method and investigation of the convergence of certain types of double trigonometric series. Computational expressions are given for the case of summation in a rectangular domain.
ISSN:0041-5553
DOI:10.1016/0041-5553(78)90161-1