Grid method for computation of generalized spheroidal wave functions based on discrete variable representation.
Grid method for computation of generalized spheroidal wave functions based on discrete variable representation.
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DOI：
10.1103/physreve.79.036710
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发表时间：
2009-03
期刊：
影响因子：
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通讯作者：
Di Yan;Liang-You Peng;Q. Gong
中科院分区：
文献类型：
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作者：
Di Yan;Liang-You Peng;Q. Gong
本文提出了一种计算广义椭球波动方程本征值和本征函数的高精度网格方法。与以往的研究不同，我们的方法是基于扩展的球面波函数的离散变量表示的基函数从相关的勒让德多项式构造。微分算子可以在网格点上解析表示，网格点是相关勒让德多项式的零点。所得到的势矩阵是简单的对角矩阵，并直接在同一网格上进行计算。相应的微分方程，从而转化为一个小矩阵的特征值问题，其特征值和特征向量收敛非常快。然后，波函数可以准确地估计在任何期望的点从展开公式与计算的本征向量。与以前的方法相比，我们的方法是直接和有效的任何参数c，无论是小或大。
We present an efficient and accurate grid method for computations of eigenvalues and eigenfunctions of the generalized spheroidal wave equation. Different from previous studies, our method is based on the expansion of the spheroidal wave function by discrete-variable-representation basis functions constructed from the associated Legendre polynomials. The differential operator can be expressed analytically on the grid points, which are the zeros of the associated Legendre polynomials. The resultant potential matrix is simply diagonal and evaluated directly on the same grid. The corresponding differential equation is thus converted to an eigenvalue problem of a small matrix, whose eigenvalues and eigenvectors are converged very fast. The wave functions can then be evaluated accurately at any desired point from the expansion formula with the computed eigenvectors. Compared to previous methods, our method is direct and efficient for any parameter c , either small or large.