Finster, Felix and Smoller, Joel (2010) Error Estimates for Approximate Solutions of the Riccati Equation with Real or Complex Potentials. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 197 (3). pp. 985-1009. ISSN 0003-9527,
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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 gluing 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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | PERTURBATIONS; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Felix Finster |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 13 Jul 2020 09:45 |
| Last Modified: | 13 Jul 2020 09:45 |
| URI: | https://pred.uni-regensburg.de/id/eprint/24201 |
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