论文标题
奇异schrödinger方程的高级特征值的准确光谱搭配计算
Accurate Spectral Collocation Computation of High Order Eigenvalues for Singular Schrödinger Equations
论文作者
论文摘要
我们关注一些经典光谱搭配方法以及新的软件系统Chebfun计算单数和常规Schr Odinger Eigenproblems的高级特征。我们希望强调这些方法的质量和缺点，并与通常的方法一起评估它们。为了解决边界奇点，我们将Chebfun与域截断一起使用。尽管它适用于光谱搭配，但一种特殊的技术和坐标变换的特殊技术，它是特殊的成分。分析了一组具有挑战性的“基准问题”（f。d。d。计算特征值，并提示我们对几乎多个特征值以及混合频谱问题的问题特别关注。
We are concerned with the study of some classical spectral collocation methods as well as with the new software system Chebfun in computing high order eigenpairs of singular and regular Schrodinger eigenproblems. We want to highlight both the qualities as well as the shortcomings of these methods and evaluate them in conjunction with the usual ones. In order to resolve a boundary singularity we use Chebfun with domain truncation. Although it is applicable with spectral collocation, a special technique to introduce boundary conditions as well as a coordinate transform, which maps an unbounded domain to a finite one, are the special ingredients. A challenging set of \hard"benchmark problems, for which usual numerical methods (f. d., f. e. m., shooting etc.) fail, are analyzed. In order to separate \good"and \bad"eigenvalues we estimate the drift of the set of eigenvalues of interest with respect to the order of approximation and/or scaling of domain parameter. It automatically provides us with a measure of the error within which the eigenvalues are computed and a hint on numerical stability. We pay a particular attention to problems with almost multiple eigenvalues as well as to problems with a mixed spectrum.
