13 citations · 40 across the 7 of their papers we have counts for
7 papers
Which Saddles Contribute? The South-East Rule for Multidimensional Integrals
Inês Aniceto, Job Feldbrugge, Christopher J. Howls
In this paper, we introduce and demonstrate a simple geometric algorithm to determine which critical points, both complex as well as real, contribute to the asymptotic evaluation o…
Appearance of the higher-order Stokes phenomenon in a discrete Airy equation
Aaron J. Moston-Duggan, Christopher J. Howls, Christopher J. Lustri
We study a discrete variant of the Airy equation, formulated as an advance-delay equation, to reveal that discretization induces the higher-order Stokes phenomenon, which is not pr…
Smoothing of the higher-order Stokes phenomenon
Chris J. Howls, John R. King, Gergő Nemes +1
For nearly a century and a half the Stokes phenomenon had been perceived as a discontinuous change in the asymptotic representation of a function. In 1989 Berry demonstrated how it…
Capturing the cascade: a transseries approach to delayed bifurcations
Inês Aniceto, Daniel Hasenbichler, Christopher J. Howls +1
Transseries expansions build upon ordinary power series methods by including additional basis elements such as exponentials and logarithms. Alternative summation methods can then b…
Globally exact asymptotics for integrals with arbitrary order saddles
Thomas Bennett, Christopher J. Howls, Gergő Nemes +1
We derive the first exact, rigorous but practical, globally valid remainder terms for asymptotic expansions about saddles and contour endpoints of arbitrary order degeneracy derive…
Aberration-like cusped focusing in the post-paraxial Talbot effect
James D Ring, Jari Lindberg, Christopher J Howls +1
We present an analysis of self-imaging in a regime beyond the paraxial, where deviation from simple paraxial propagation causes apparent self-imaging aberrations. The resulting str…
Exponential asymptotics and boundary value problems: keeping both sides happy at all orders
C. J. Howls
We introduce templates for exponential asymptotic expansions that, in contrast to matched asymptotic approaches, enable the simultaneous satisfaction of both boundary values in cla…