Numerical Reconstruction of Potentials Based on a Sequence of Inverse Sturm–Liouville Problems

Abstract

Numerical solutions to inverse Sturm–Liouville problems by three spectra, on a finite interval [Formula: see text] are considered. Dirichlet boundary conditions are assumed to hold at the end-points of the interval [Formula: see text], and either a Dirichlet or a Robin-type interior point condition is imposed at an arbitrary interior point [Formula: see text] of [Formula: see text]. We demonstrate that the numerical solution of the inverse three spectra problem corresponding to an interior point [Formula: see text] depends continuously on [Formula: see text]. This statement is particularly useful when measurements of the input data cannot be obtained at the interior point [Formula: see text], but they can be obtained at a nearby interior point. Consequently, we could solve approximately the original inverse problem by departing slightly from [Formula: see text]. We validate this statement through numerical experiments for sequences of interior points [Formula: see text] converging to [Formula: see text].