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Greenberg, L. and Marletta, M. (1997) The Validity of Richardson Extrapolation in Coefficient Approximation Methods for Fourth Order and Higher Order Self-Adjoint ODE Eigenvalue Problems. Technical Report, Department of Mathematics and Computer Science, University of Leicester, Leicester.

has been cited by the following article:

• 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.