Tag Archives: Saddle-Point

Joint use of Weniger transformation and hyperasymptotics for accurate asymptotic evaluations of a class of saddle-point integrals. II. Higher order transformations

The use of hyperasymptotics (H) and the Weniger transformation (WY) has been proposed, in a joint fashion, for decoding the divergent asymptotic series generated by the steepest descent on a wide class of saddle-point integrals evaluated across Stokes sets (Borghi, 2008). In the present sequel, the full development of the hyperasymptotic- Weniger transformation (H-WY) up to the second order in H is derived. Numerical experiments, carried out on several classes of saddle-point integrals, including the swallowtail diffraction catastrophe, show the effectiveness of the second-level H-WT, in particular  when the integrals are evaluated beyond the asymptotics realm.

Article originally published in ‘Physical Review’, V. 80(2009), n. 1, Copyright (2009) by the American Physical Society. Reprinted with permission

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