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

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