求解逆Sturm-Liouville问题的最小二乘泛函

Inversion of trace formulas for a Sturm-Liouville operator

This paper revisits the classical problem "Can we hear the density of a string?", which can be formulated as an inverse spectral problem for a Sturm-Liouville operator. Based on inverting a sequence of trace formulas, we propose a new numerical scheme to reconstruct the density. Numerical experiments are presented to verify the validity and effectiveness of the numerical scheme.

用于斯蒂姆-刘维尔问题的扩展普鲁斯方法

An Extended Pruess Method for Sturm-Liouville Problems

本文提出了一种改进的分段逼近方法，用于计算斯蒂姆-刘维尔问题的特征值。通过使用2/cos²(x)的翻译替代传统分段常数或线性势函数，得到具有基本解的特征方程。

变步长有限差分方案用于求解Sturm-Liouville问题

Variable-step finite difference schemes for the solution of Sturm-Liouville problems

本文提出高阶有限差分方案求解正则和奇异Sturm-Liouville问题，通过线性代数技术实现离散问题的数值解，并通过不同测试问题验证算法性能。

An $\mathcal{O}\left(1\right)$ algorithm for the numerical evaluation of the Sturm-Liouville eigenvalues of the spheroidal wave functions of order zero

In addition to being the eigenfunctions of the restricted Fourier operator, the angular spheroidal wave functions of the first kind of order zero and nonnegative integer characteristic exponents are the solutions of a singular self-adjoint Sturm-Liouville problem. The running time of the standard algorithm for the numerical evaluation of their Sturm-Liouville eigenvalues grows with both bandlimit and characteristic exponent. Here, we describe a new approach whose running time is bounded independent of these parameters. Although the Sturm-Liouville eigenvalues are of little interest themselves,…

双指数Sinc列点法用于奇异Sturm-Liouville问题

The Double Exponential Sinc Collocation Method for Singular Sturm-Liouville Problems

本文提出一种高效准确的计算奇异Sturm-Liouville边值问题特征值的方法，结合双指数公式与Sinc列点法，实现指数收敛率。

Sturm-Liouville特征值问题谱解的数值计算

Numerical computation of spectral solutions for Sturm-Liouville eigenvalue problems

针对Sturm-Liouville特征值问题，提出基于Chebfun软件算法结合区域截断的离散方法以计算高阶特征值，数值实验验证了该方法的高效性。