Stability chart of Hill's equation by a Sturm-Liouville approach

Abstract

This paper introduces a Sturm-Liouville based algorithm to compute the stability chart of Hill's equation. It will be shown that finding the borders of the instability tongues of Hill's equation can be set as a Sturm-Liouville boundary value problem, and how this problem can be set as an eigenvalue-eigenvector problem of a differential matrix LH using a finite-difference approximation of the first and second derivatives of a scalar function.