Recovering Boundary Conditions In Inverse Sturm-Liouville Problems
RECENT ADVANCES IN DIFFERENTIAL EQUATIONS AND MATHEMATICAL PHYSICS(2006)
Abstract
We introduce a variational algorithm, which solves the classical inverse Sturm-Liouville problem when two spectra are given. In contrast to other approaches, it recovers the potential as well as the boundary conditions without a priori knowledge of the mean of the potential. Numerical. examples show that the algorithm works quite reliable, even in the presence of noise. A proof of the absence of strict local minimizers of the functional supports the observation, that a good initial guess is not essential.
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Key words
boundary condition,a priori knowledge,numerical analysis,sturm liouville problem
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