Abstract A new numerical method to solve two-point boundary value problems for second order differential equations is proposed. This method is based on the singular value expansion of an integral formulation of the derivative operator. Here, we outline such an expansion and we propose a method to build new algebraic schemes able to solve boundary value problems. The performances of the presented method are tested by numerical experiments on boundary value problems that have known solutions.

中文翻译：

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一种求解边值问题的谱方法

摘要 提出了一种求解二阶微分方程两点边值问题的新数值方法。该方法基于导数算子积分公式的奇异值展开。在这里，我们概述了这种扩展，并提出了一种构建能够解决边值问题的新代数方案的方法。通过对已知解的边值问题的数值实验来测试所提出方法的性能。