TITLE:
Eigenvalue Computation of Regular 4th Order Sturm-Liouville Problems
AUTHORS:
Ahmad Alalyani
KEYWORDS:
4th Order Sturm-Liouville Problem, Magnus Methods (MG4), Regular Boundary Conditions
JOURNAL NAME:
Applied Mathematics,
Vol.10 No.9,
September
26,
2019
ABSTRACT: In this paper we present and test a numerical method for computing eigenvalues of 4th order Sturm-Liouville (SL) differential operators on finite intervals with regular boundary conditions. This method is a 4th order shooting method based on Magnus expansions (MG4) which use MG4 shooting as the integrator. This method is similar to the SLEUTH (Sturm-Liouville Eigenvalues Using Theta Matrices) method of Greenberg and Marletta which uses the 2nd order Pruess method (also known as the MG2 shooting method) for the integrator. This method often achieves near machine precision accuracies, and some comparisons of its performance against the well-known SLEUTH software package are presented.