The recovery of analytic potentials for fourth-order differential equations

Abstract

We present a new numerical method to solve the inverse spectral problem for the fourth-order differential operator based on the identification of the Taylor coefficients of an analytic solution. We show that an analytic potential can be recovered from the knowledge of four spectra and prove that convergence follows from the exponential growth of the solution. The solution is obtained by a sequential algorithm by which four Taylor coefficients of the potential are recovered explicitly at each iteration.

Keywords:

• Inverse problems
• Analytic potentials
• Differential equations
• 1991 Mathematics Subject Classification:
• 34A55