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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.18406 |
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| _version_ | 1866912350683004928 |
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| author | Arnold, Anton Körner, Jannis |
| author_facet | Arnold, Anton Körner, Jannis |
| contents | This paper introduces an efficient high-order numerical method for solving the 1D stationary Schrödinger equation in the highly oscillatory regime. Building upon the ideas from [Arnold, Ben Abdallah, Negulescu, SIAM J. Numer. Anal., 2011], we first analytically transform the given equation into a smoother (i.e. less oscillatory) equation. By developing sufficiently accurate quadratures for several (iterated) oscillatory integrals occurring in the Picard approximation of the solution, we obtain a one-step method that is third order w.r.t. the step size. The accuracy and efficiency of the method are illustrated through several numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_18406 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | WKB-based third order method for the highly oscillatory 1D stationary Schrödinger equation Arnold, Anton Körner, Jannis Numerical Analysis 34E20, 81Q20, 65L11, 65M70 This paper introduces an efficient high-order numerical method for solving the 1D stationary Schrödinger equation in the highly oscillatory regime. Building upon the ideas from [Arnold, Ben Abdallah, Negulescu, SIAM J. Numer. Anal., 2011], we first analytically transform the given equation into a smoother (i.e. less oscillatory) equation. By developing sufficiently accurate quadratures for several (iterated) oscillatory integrals occurring in the Picard approximation of the solution, we obtain a one-step method that is third order w.r.t. the step size. The accuracy and efficiency of the method are illustrated through several numerical examples. |
| title | WKB-based third order method for the highly oscillatory 1D stationary Schrödinger equation |
| topic | Numerical Analysis 34E20, 81Q20, 65L11, 65M70 |
| url | https://arxiv.org/abs/2402.18406 |