102 citations · 534 across the 14 of their papers we have counts for
14 papers
Runge-Kutta-Gegenbauer explicit methods for advection-diffusion problems
Stephen O'Sullivan
In this paper, Runge-Kutta-Gegenbauer (RKG) stability polynomials of arbitrarily high order of accuracy are introduced in closed form. The stability domain of RKG polynomials exten…
Strong-field tidal distortions of rotating black holes: III. Embeddings in hyperbolic 3-space
Robert F. Penna, Scott A. Hughes, Stephen O'Sullivan
In previous work, we developed tools for quantifying the tidal distortion of a black hole's event horizon due to an orbiting companion. These tools use techniques which require lar…
Factorized Runge-Kutta-Chebyshev Methods
Stephen O'Sullivan
The second-order extended stability Factorized Runge-Kutta-Chebyshev (FRKC2) class of explicit schemes for the integration of large systems of PDEs with diffusive terms is presente…
A class of high-order Runge-Kutta-Chebyshev stability polynomials
Stephen O'Sullivan
The analytic form of a new class of factorized Runge-Kutta-Chebyshev (FRKC) stability polynomials of arbitrary order is presented. Roots of FRKC stability polynomials of degree…
Strong-field tidal distortions of rotating black holes: II. Horizon dynamics from eccentric and inclined orbits
Stephen O'Sullivan, Scott A. Hughes
In a previous paper, we developed tools for studying the horizon geometry of a Kerr black hole that is tidally distorted by a binary companion using techniques that require large m…
Strong-field tidal distortions of rotating black holes: Formalism and results for circular, equatorial orbits
Stephen O'Sullivan, Scott A. Hughes
Tidal coupling between members of a compact binary system can have an interesting and important influence on that binary's dynamical inspiral. Tidal coupling also distorts the bina…