This paper focuses on the study of Sturm-Liouville eigenvalue problems. In the classical Chebyshev collocation method, the Sturm-Liouville problem is discretized to a generalized eigenvalue problem where the functions represent interpolants in suitably rescaled Chebyshev points. We are concerned with the computation of high-order eigenvalues of Sturm-Liouville problems using an effective method of discretization based on the Chebfun software algorithms with domain truncation. We solve some numerical Sturm-Liouville eigenvalue problems and demonstrate the computations' efficiency.

翻译：本文聚焦于Sturm-Liouville特征值问题的研究。在经典的Chebyshev配点法中，Sturm-Liouville问题被离散化为广义特征值问题，其中函数表示在适当重新标度的Chebyshev点上的插值函数。我们基于Chebfun软件算法，采用区域截断的有效离散化方法，研究Sturm-Liouville问题高阶特征值的计算。通过求解若干数值Sturm-Liouville特征值问题，验证了该计算方法的有效性。