The transmutation operator method for efficient solution of the inverse Sturm-Liouville problem on a half-line

摘要

The inverse Sturm-Liouville problem on a half-line is considered. With the aid of a Fourier-Legendre series representation of the transmutation integral kernel and the Gel'fand-Levitan equation, the numerical solution of the problem is reduced to a system of linear algebraic equations. The potential q is recovered from the first coefficient of the Fourier-Legendre series. The resulting numerical method is direct and simple. The results of the numerical experiments are presented.