Eigenparameter Dependent Inverse Sturm-Liouville Problems
نویسندگان
چکیده
Uniqueness of and numerical techniques for the inverse Sturm-Liouville problem with eigenparameter dependent boundary conditions will be discussed. We will use a Gel’fand-Levitan technique to show that the potential q in u00 þ qu 1⁄4 u, 0 < x < 1 uð0Þ 1⁄4 0, ða þ bÞuð1Þ 1⁄4 ðc þ d Þu0ð1Þ can be uniquely determined using spectral data. In the presence of finite spectral data, q can be reconstructed using a successive approximation method that involves solving a hyperbolic boundary value problem that arises in the the Gel’fand-Levitan analysis. We also consider a shooting method where the right endpoint boundary condition is used in conjunction with a quasi-Newton scheme to recover the unknown potential, q.
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