Abstract
In this paper we propose a method to reconstruct the potential of an inverse fourth-order Sturm-Liouville problem from three spectra. The purpose of the method is to look for a continuous approximation of the unknown potential belonging to a suitable finite dimensional function space. A method to solve the direct Sturm-Liouville problem of fourth order must be used to compute the corresponding eigenvalues of the potential which is step by step updated during the Broyden iteration. This can be done by using modified Numerov’s method or boundary value methods which were recently introduced by the authors in [1]. Numerical experiments illustrate the performance of the approach.
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