论文标题
解决反向Sturm-Liouville问题的直接方法
A direct method for solving inverse Sturm-Liouville problems
论文作者
论文摘要
我们考虑了两个主要的逆向liouville问题：从两个光谱或光谱密度函数中恢复电位和边界条件的问题。基于变速箱操作员方法，新的Neumann系列贝塞尔功能表示解决方案和Gelfand-Levitan方程的新型Neumann系列的诺伊曼（Neumann）系列，开发了一种实用解决方案的简单方法。该方法允许人们将逆sturm-liouville问题直接减少到线性代数方程系统中，从而使电势从溶液向量的第一个元素中恢复。我们证明了该方法的稳定性，并通过几个数值示例显示了其数值效率。
We consider two main inverse Sturm-Liouville problems: the problem of recovery of the potential and the boundary conditions from two spectra or from a spectral density function. A simple method for practical solution of such problems is developed, based on the transmutation operator approach, new Neumann series of Bessel functions representations for solutions and the Gelfand-Levitan equation. The method allows one to reduce the inverse Sturm-Liouville problem directly to a system of linear algebraic equations, such that the potential is recovered from the first element of the solution vector. We prove the stability of the method and show its numerical efficiency with several numerical examples.
