High Order Finite Difference Schemes for the Numerical Solution of Eigenvalue Problems for IVPs in ODEs

In this short note we describe how to apply high order finite difference methods to the solution of eigenvalue problems with initial conditions. Finite differences have been successfully applied to both second order initial and boundary value problems in ODEs. Here, based on the results previously obtained, we outline an algorithm that at first computes a good approximation of the eigenvalues of a linear second order differential equation with initial conditions. Then, for any given eigenvalue, it determines the associated eigenfunction.