A collocation method based on Bernoulli polynomial is developed to compute the eigenvalues and eigenfunctions of some known fourth-order Sturm-Liouville problems. Properties of Bernoulli matrix method are presented to convert the problem into a system of linear algebraic equations. Error estimation is introduced. The eigenfunctions are calculated for the test problems. A comparison is made with other relevant studies.

中文翻译：

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伯努利级数与切比雪夫并置点的四阶sturm-liouville问题的特征值和特征函数

提出了一种基于伯努利多项式的搭配方法，以计算一些已知的四阶Sturm-Liouville问题的特征值和特征函数。提出了伯努利矩阵方法的性质，以将问题转换为线性代数方程组。引入误差估计。针对测试问题计算本征函数。与其他相关研究进行了比较。