论文标题
在修改后的第二个潘恩 - 戴霍格·安德森边界价值问题上
On modified second Paine-de Hoog-Anderssen boundary value problem
论文作者
论文摘要
本文讨论了Sturm-Liouville边界价值问题（BVP）的特殊情况，这是一个特征值问题，其特征是Sturm-liouville差异操作员带有未知光谱和相关特征性功能。通过以Schrödinger形式检查BVP，我们对相应不变函数采用相互二次形式的形式的问题感兴趣。我们称此BVP为修改后的第二个Paine-de Hoog-Anderssen（PDHA）问题。我们在不解决特征值问题的情况下估计最低阶的特征值，而是利用局部景观和有效的潜在功能。尽管对于特定的参数值组合（频谱估计值表现出较差的质量），但结果通常可以接受，尽管它们高估了数值计算。从定性上讲，特征值估计值非常出色，并且该提案可以针对其他BVP。
This article deals with a special case of the Sturm-Liouville boundary value problem (BVP), an eigenvalue problem characterized by the Sturm-Liouville differential operator with unknown spectra and the associated eigenfunctions. By examining the BVP in the Schrödinger form, we are interested in the problem where the corresponding invariant function takes the form of a reciprocal quadratic form. We call this BVP the modified second Paine-de Hoog-Anderssen (PdHA) problem. We estimate the lowest-order eigenvalue without solving the eigenvalue problem but by utilizing the localized landscape and effective potential functions instead. While for particular combinations of parameter values that the spectrum estimates exhibit a poor quality, the outcomes are generally acceptable although they overestimate the numerical computations. Qualitatively, the eigenvalue estimate is strikingly excellent, and the proposal can be adopted to other BVPs.
