Bernstein spectral method for quasinormal modes and other eigenvalue problems
Abstract Spectral methods are now common in the solution of ordinary differential eigenvalue problems in a wide variety of fields, such as in the computation of black hole quasinormal modes. Most of these spectral codes are based on standard Chebyshev, Fourier, or some other orthogonal basis functio...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-12-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-023-12350-9 |
| _version_ | 1797233343987712000 |
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| author | Sean Fortuna Ian Vega |
| author_facet | Sean Fortuna Ian Vega |
| author_sort | Sean Fortuna |
| collection | DOAJ |
| description | Abstract Spectral methods are now common in the solution of ordinary differential eigenvalue problems in a wide variety of fields, such as in the computation of black hole quasinormal modes. Most of these spectral codes are based on standard Chebyshev, Fourier, or some other orthogonal basis functions. In this work we highlight the usefulness of a relatively unknown set of non-orthogonal basis functions, known as Bernstein polynomials, and their advantages for handling boundary conditions in ordinary differential eigenvalue problems. We also report on a new user-friendly package, called SpectralBP, that implements Berstein-polynomial-based pseudospectral routines for eigenvalue problems. We demonstrate the functionalities of the package by applying it to a number of model problems in quantum mechanics and to the problem of computing scalar and gravitational quasinormal modes in a Schwarzschild background. We validate our code against some known results and achieve excellent agreement. Compared to continued-fraction or series methods, global approximation methods are particularly well-suited for computing purely imaginary modes such as the algebraically special modes for Schwarzschild gravitational perturbations. |
| first_indexed | 2024-03-08T18:15:50Z |
| format | Article |
| id | doaj.art-aabdae32d04e4b1e882d9efd6d4b5955 |
| institution | Directory Open Access Journal |
| issn | 1434-6052 |
| language | English |
| last_indexed | 2024-04-24T16:14:40Z |
| publishDate | 2023-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj.art-aabdae32d04e4b1e882d9efd6d4b59552024-03-31T11:31:26ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522023-12-01831212710.1140/epjc/s10052-023-12350-9Bernstein spectral method for quasinormal modes and other eigenvalue problemsSean Fortuna0Ian Vega1National Institute of Physics, University of the Philippines DilimanNational Institute of Physics, University of the Philippines DilimanAbstract Spectral methods are now common in the solution of ordinary differential eigenvalue problems in a wide variety of fields, such as in the computation of black hole quasinormal modes. Most of these spectral codes are based on standard Chebyshev, Fourier, or some other orthogonal basis functions. In this work we highlight the usefulness of a relatively unknown set of non-orthogonal basis functions, known as Bernstein polynomials, and their advantages for handling boundary conditions in ordinary differential eigenvalue problems. We also report on a new user-friendly package, called SpectralBP, that implements Berstein-polynomial-based pseudospectral routines for eigenvalue problems. We demonstrate the functionalities of the package by applying it to a number of model problems in quantum mechanics and to the problem of computing scalar and gravitational quasinormal modes in a Schwarzschild background. We validate our code against some known results and achieve excellent agreement. Compared to continued-fraction or series methods, global approximation methods are particularly well-suited for computing purely imaginary modes such as the algebraically special modes for Schwarzschild gravitational perturbations.https://doi.org/10.1140/epjc/s10052-023-12350-9 |
| spellingShingle | Sean Fortuna Ian Vega Bernstein spectral method for quasinormal modes and other eigenvalue problems European Physical Journal C: Particles and Fields |
| title | Bernstein spectral method for quasinormal modes and other eigenvalue problems |
| title_full | Bernstein spectral method for quasinormal modes and other eigenvalue problems |
| title_fullStr | Bernstein spectral method for quasinormal modes and other eigenvalue problems |
| title_full_unstemmed | Bernstein spectral method for quasinormal modes and other eigenvalue problems |
| title_short | Bernstein spectral method for quasinormal modes and other eigenvalue problems |
| title_sort | bernstein spectral method for quasinormal modes and other eigenvalue problems |
| url | https://doi.org/10.1140/epjc/s10052-023-12350-9 |
| work_keys_str_mv | AT seanfortuna bernsteinspectralmethodforquasinormalmodesandothereigenvalueproblems AT ianvega bernsteinspectralmethodforquasinormalmodesandothereigenvalueproblems |