Recovery of Inhomogeneity from Output Boundary Data

We consider the Sturm–Liouville equation on a finite interval with real-valued integrable potential and propose method for solving following general inverse problem. recover from given set of output boundary values solution satisfying some known initial conditions spectral parameter. Special cases this problem include recovery Weyl function, two-spectra problem, as well plane wave that interacted potential. The is based special Neumann series Bessel functions representations solutions equations. With their aid, reduced to classical recovering two spectra, which solved again help same representations. overall approach leads an efficient numerical algorithm Its efficiency illustrated by several examples.