Abstract. This paper examines and extends a method, recently proposed by the author, for recovering from eigenvalues a symmetric potential of a Sturm–Liouville operator with Dirichlet boundary conditions. It uses Numerov's method and an extension by Andrew and Paine of an asymptotic correction technique of Paine, de Hoog and Anderssen. The method is extended to deal with natural boundary conditions and its convergence properties are investigated. Numerical results show that the method can extract more information from a given set of data than a related earlier method which uses a second-order discretization of the differential equation. Non-symmetric problems are also considered.

Print publication: Issue 1 (February 2005)
Received 2 August 2004, in final form 3 November 2004
Published 6 December 2004