Numerical reconstruction in a three-spectra inverse Sturm-Liouville problem with mixed boundary conditions

作者：Drignei Mihaela Cristina^*

来源：Inverse Problems in Science and Engineering, 2013, 21(8): 1368-1391.

DOI：10.1080/17415977.2013.764603

• inverse Sturm-Liouville problem
• spectra
• Goursat boundary value problem
• Gelfand-Levitan-Marchenko kernel

This paper proposes an algorithm for the numerical reconstruction of the coefficient (also called 'potential') function q in the canonical Sturm-Liouville differential operator L-(q) [u] := -u '' + q(x) u from three known sequences of its eigenvalues. These correspond respectively to three sets of mixed boundary conditions: Dirichlet type for the interval [0, a], Dirichlet-Robin type for the interval [0, a(0)] and Robin-Dirichlet type for the interval [a(0), a], where a(0) is an interior point of the interval [0, a]. This problem originates in an engineering application involving a string and its frequencies of oscillations when set into vibration. The method will be illustrated with numerical examples including both continuous and discontinuous potential functions.

• 出版日期2013