求解具有特殊奇异微分算子的Sturm-Liouville问题的FD方法
The FD-method for solving Sturm-Liouville problems with special singular differential operator
AI总结：
提出一种超指数收敛的数值解析方法（FD方法），用于求解一类带边界条件的奇异微分算子的特征值问题，并给出收敛性证明与数值验证。
摘要：
本文描述了一种超指数收敛的数值解析方法，用于求解一类带边界条件的奇异微分算子的特征值问题。该方法（FD方法）由V. L. Makarov首次提出，成功结合了系数逼近方法（CAM）和同伦方法的优点。文中陈述并严格证明了保证所提方法收敛的充分条件。还描述了所提方法的软件实现算法。文中包含大量数值算例，这些算例证实了理论结论。我们还将FD方法得到的结果与求解Sturm-Liouville问题的强大软件包SLEIGN2的结果进行了比较。
英文摘要：
In the paper we describe a superexponentially convergent numerical-analytical method for solving the eigenvalue problem for the some class of singular differential operators with boundary conditions. The method (FD-method) was firstly proposed by V. L. Makarov and successfully combines the benefits of using the {\it coefficient approximation methods} (CAM) and the homotopy approach. The sufficient conditions which provides convergence of the proposed method are stated and rigorously substantiated. The algorithm for the software implementation of the proposed method is described too. A lot of numerical examples are included in the paper. The examples confirm the theoretical conclusions. We also have made the comparison between the results obtained by FD-method and results obtained by the powerful software package for solving Sturm-Liouville problems --- SLEIGN2.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
