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- W4308593014 abstract "Abstract We consider the highly oscillatory integral for large positive values of w , , K and p positive integers with , and an entire function. The standard saddle point method is complicated and we use here a simplified version of this method introduced by López et al. We derive an asymptotic approximation of this integral when for general values of K and p in terms of elementary functions, and determine the Stokes lines. For , the asymptotic behavior of this integral may be classified in four different regions according to the even/odd character of the couple of parameters K and p ; the special case requires a separate analysis. As an important application, we consider the family of canonical catastrophe integrals for large values of one of its variables, say , and bounded values of the remaining ones. This family of integrals may be written in the form for appropriate values of the parameters w , θ and the function . Then, we derive an asymptotic approximation of the family of canonical catastrophe integrals for large . The approximations are accompanied by several numerical experiments. The asymptotic formulas presented here fill up a gap in the NIST Handbook of Mathematical Functions by Olver et al." @default.
- W4308593014 created "2022-11-12" @default.
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- W4308593014 date "2022-11-07" @default.
- W4308593014 modified "2023-10-16" @default.
- W4308593014 title "Asymptotic approximation of a highly oscillatory integral with application to the canonical catastrophe integrals" @default.
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- W4308593014 doi "https://doi.org/10.1111/sapm.12539" @default.
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