Eigenparameter Dependent Inverse Sturm-Liouville Problems
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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 - u″ + qu = λu, 0 < x < I u(0) = 0, (aλ + b)u(1) = (cλ + d)u′(1) 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.
author list (cited authors)
McCarthy, C. M., & Rundell, W.