TRANSMUTATION OPERATORS METHOD FOR STURM-LIOUVILLE EQUATIONS IN IMPEDANCE FORM II: INVERSE PROBLEM

Abstract

The inverse spectral problem for the Sturm-Liouville equation in impedance form is considered. A corresponding Gelfand-Levitan integral equation is derived. A Fourier-Legendre series expansion for the transmutation operator kernel combined with the Gelfand-Levitan equation leads to a simple direct method for solving the inverse problem of recovering the impedance function from spectral data by solving a system of linear algebraic equations, such that the impedance function is recovered from the first element of the solution vector. The stability of the method is proved. Its numerical performance is illustrated by several examples.