Numerical solution of inverse Sturm--Liouville problems

Abstract

A new algorithm is proposed for solving the inverse Sturm--Liouville problem of reconstructing a symmetric potential from eigenvalues. It uses Numerov's method instead of the second order method of the related algorithm of Fabiano, Knobel and Lowe. An extension by Andrew and Paine of the asymptotic correction technique of Paine, de Hoog and Anderssen is the key to the success of the new algorithm. Numerical results show that it can produce good accuracy even from very limited data.