Error Estimates for Approximate Solutions of the Riccati Equation with Real or Complex Potentials

Details Error Estimates for Approximate Solutions of the Riccati Equation with Real or Complex Potentials Error Estimates for Approximate Solutions of the Riccati Equation with Real or Complex Potentials

2008-07-28

arxiv.org/abs/0807.4406v2

Arch. Rational Mech. Anal. 197 (2010) 985-1009

Physics

Mathematical Physics

23 pages, LaTeX, 13 figures, minor improvements (published version)

Scientific paper

10.1007/s00205-010-0301-2

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.

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