Methods and Applications of Analysis

Volume 22 (2015)

Number 1

Refined error estimates for the Riccati equation with applications to the angular Teukolsky equation

Pages: 67 – 100

DOI: https://dx.doi.org/10.4310/MAA.2015.v22.n1.a3

Authors

Felix Finster (Fakultät für Mathematik, Universität Regensburg, Germany)

Joel Smoller (Department of Mathematics, University of Michigan, Ann Arbor, Mich., U.S.A.)

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

error estimates, Riccati equation, Sturm-Liouville equations, angular Teukolsky equation

2010 Mathematics Subject Classification

34A30, 34A45, 34E20

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Published 1 April 2015