Modified Numerov’s method for inverse Sturm–Liouville problems
| Autor: | Zhengda Huang, Xiaoliang Cheng, Qin Gao |
|---|---|
| Rok vydání: | 2013 |
| Předmět: |
Applied Mathematics
Mathematical analysis Sturm–Liouville theory Mathematics::Spectral Theory Numerov's method Computational Mathematics symbols.namesake Operator (computer programming) Dirichlet boundary condition Convergence (routing) symbols Boundary value problem Eigenvalues and eigenvectors Interpolation Mathematics |
| Zdroj: | Journal of Computational and Applied Mathematics. 253:181-199 |
| ISSN: | 0377-0427 |
| DOI: | 10.1016/j.cam.2013.04.025 |
| Popis: | In this paper, we propose a new modified Numerov's method for recovering from eigenvalues a symmetric potential of a Sturm-Liouville operator with Dirichlet boundary conditions. We use interpolation to refine the mesh sufficiently for Numerov's method to be effective even without the asymptotic correction technique of Andrew and Paine. Accuracy and stability of the method are investigated. Convergence of the method is established. Our method is extended to deal with natural boundary conditions. Numerical experiments confirm its competitiveness. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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