Refined Error Estimates for the Riccati Equation with Applications to the Angular Teukolsky Equation
Classical Analysis and ODEs
2016-03-14 v3 General Relativity and Quantum Cosmology
Mathematical Physics
math.MP
Abstract
We derive refined rigorous error estimates for approximate solutions of Sturm-Liouville and Riccati equations with real or complex potentials. The approximate solutions include WKB approximations, Airy and parabolic cylinder functions, and certain Bessel functions. Our estimates are applied to solutions of the angular Teukolsky equation with a complex aspherical parameter in a rotating black hole Kerr geometry.
Keywords
Cite
@article{arxiv.1307.6470,
title = {Refined Error Estimates for the Riccati Equation with Applications to the Angular Teukolsky Equation},
author = {Felix Finster and Joel Smoller},
journal= {arXiv preprint arXiv:1307.6470},
year = {2016}
}
Comments
34 pages, LaTeX, 4 figures, 4 ancillary files, minor corrections (published version)