The Sturm-Liouville problem (SLP) in the general form is considered. The numerical solution of the SLP can be obtained using shooting to calculate an eigenvalue approximation as a solution of a suitable nonlinear equation and then computing the corresponding eigenfunction. We use the shooting method both for eigenvalues and eigenfunctions as well. In integrating the corresponding initial value problems (IVPs) we resort to the boundary value method. The technique proposed seems to be well suited to supplying a general formula for the global discretization error (GDE) of the eigenfunctions depending on the discretization errors arising from the numerical integration of the IVPs. The estimate of the GDE can be used to correct the discrete approximation of the eigenfunctions. A technique to estimate the eigenvalues error is also suggested. Numerical experiments concerning some classical SLPs are presented.

Joint work with G.Gheri and M.Marletta

MINISIMPOSIUM SESSION: 6. Novel methods for ODEs