Optical asymptotics via Weniger transformation

Details Optical asymptotics via Weniger transformation Optical asymptotics via Weniger transformation

2007-06-25

arxiv.org/abs/0706.3573v1

Physics

Optics

4 pages, 1 figure

Scientific paper

Starting from the resurgence equation discovered by Berry and Howls [M. V. Berry and C. Howls "Hyperasymptotics for integrals with saddles," Proc. R. Soc. Lond. A 434, 657-675 (1991)], the Weniger transformation is here proposed as a natural, efficient, and straightforwardly implementable scheme for the efficient asymptotics evaluation of a class of integrals occurring in several areas of physics and, in particular, of optics. Preliminary numerical tests, carried out on the Pearcey function, provide a direct comparison between the performances of Weniger transformation and those of Hyperasymptotics, which seems to corroborate the theoretical predictions. We believe that Weniger transformation would be a very useful computational tool for the asymptotic treatment of several optical problems.

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