Error Estimates for Approximate Solutions of the Riccati Equation with Real or Complex Potentials
Mathematical Physics
2010-08-18 v2 Analysis of PDEs
Classical Analysis and ODEs
math.MP
Numerical Analysis
Abstract
A method is presented for obtaining rigorous error estimates for approximate solutions of the Riccati equation, with real or complex potentials. Our main tool is to derive invariant region estimates for complex solutions of the Riccati equation. We explain the general strategy for applying these estimates and illustrate the method in typical examples, where the approximate solutions are obtained by glueing together WKB and Airy solutions of corresponding one-dimensional Schrodinger equations. Our method is motivated by and has applications to the analysis of linear wave equations in the geometry of a rotating black hole.
Keywords
Cite
@article{arxiv.0807.4406,
title = {Error Estimates for Approximate Solutions of the Riccati Equation with Real or Complex Potentials},
author = {Felix Finster and Joel Smoller},
journal= {arXiv preprint arXiv:0807.4406},
year = {2010}
}
Comments
23 pages, LaTeX, 13 figures, minor improvements (published version)