论文标题
使用Chebyshev网格的矩阵方法实现
An implementation of the matrix method using Chebyshev grid
论文作者
论文摘要
在这项工作中，我们探讨了矩阵方法在非均匀网格上用于黑洞准模式的特性。特别是，该方法被实施以适应Chebyshev网格，旨在有效抑制Runge的现象。据发现，尽管从数学的角度来看，这种实现是有利的，但实际上，精度的提高并不一定弥补计算时间中的罚款。另一方面，原始矩阵方法虽然符合Runge的现象，但对于大多数具有中等网格数的应用来说是合理的，并且足以满足。在计算时间并获得了重要的数字方面，我们对两个方面之间的权衡进行了分析。还解决了本研究的含义。
In this work, we explore the properties of the matrix method for black hole quasinormal modes on the nonuniform grid. In particular, the method is implemented to be adapted to the Chebyshev grid, aimed at effectively suppressing Runge's phenomenon. It is found that while such an implementation is favorable from a mathematical point of view, in practice, the increase in precision does not necessarily compensate for the penalty in computational time. On the other hand, the original matrix method, though subject to Runge's phenomenon, is shown to be reasonably robust and suffices for most applications with a moderate grid number. In terms of computational time and obtained significant figures, we carried out an analysis regarding the trade-off between the two aspects. The implications of the present study are also addressed.
