Spectrum completion and inverse Sturm–Liouville problems

Given a finite set of eigenvalues regular Sturm-Liouville problem for the equation -y{\prime}{\prime}+q(x)y={\lambda}y, potential q(x) which is unknown. We show possibility to compute more without any additional information on q(x). Moreover, considering with boundary conditions y{\prime}(0)-hy(0)=0 and y{\prime}({\pi})+Hy({\pi})=0, where h, H are some constants, we complete its spectrum neither nor constants h H. The computed uniform absolute accuracy. Based this result propose new method numerical solution inverse recovering from two spectra. includes completion spectra in first step reduction system linear algebraic equations second. recovered component vector. approach based special Neumann series Bessel functions representations solutions possessing remarkable properties leads an efficient algorithm solving problems.