论文标题
伯恩斯坦光谱法，用于准模式和其他特征值问题
Bernstein spectral method for quasinormal modes and other eigenvalue problems
论文作者
论文摘要
现在，在各种领域的普通差分特征值问题的解决方案中，频谱方法现在很常见，例如在黑洞准模式的计算中。这些光谱代码大多数基于标准的Chebyshev，傅立叶或其他正交函数。在这项工作中，我们强调了一组相对未知的非正交基函数（称为伯恩斯坦多项式）的有用性，以及它们在普通差分特征值问题中处理边界条件的优势。我们还报告了一个新的用户友好软件包，称为\ texttt {SpectralBp}，该软件包实现了基于BersteN-polynomial的伪谱例程，以解决特征值问题。我们通过将包装应用于量子力学中的许多模型问题以及计算标量和重力的准模式中的问题来证明包装的功能。我们根据一些已知结果验证代码，并实现出色的一致性。与续分或串联方法相比，全局近似方法特别适合计算纯虚构模式，例如用于Schwarzschild引力扰动的代数特殊模式。
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 \texttt{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.
