All posts by Prof. Riccardo Borghi

About Prof. Riccardo Borghi

Università degli StudiRoma Tre Rome Italy

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

View full article in PDF