Matrix methods for computing Eigenvalues of Sturm-Liouville problems of order four

  • This paper examines and develops matrix methods to approximate the eigenvalues of a fourth order Sturm-Liouville problem subjected to a kind of fixed boundary conditions, furthermore, it extends the matrix methods for a kind of general boundary conditions. The idea of the methods comes from finite difference and Numerov's method as well as boundary value methods for second order regular Sturm-Liouville problems. Moreover, the determination of the correction term formulas of the matrix methods are investigated in order to obtain better approximations of the problem with fixed boundary conditions since the exact eigenvalues for q = 0 are known in this case. Finally, some numerical examples are illustrated.

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Author:Amornrat Rattana, Christine Böckmann
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Potsdam (1(2012)13)
Document Type:Preprint
Date of Publication (online):2012/04/25
Year of Completion:2012
Publishing Institution:Universität Potsdam
Release Date:2012/04/25
Tag:Boundary value methods; Eigenvalues; Finite difference method; Fourth order Sturm-Liouville problem; Numerov's method
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC Classification:34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Bxx Boundary value problems (For ordinary differential operators, see 34Lxx) / 34B09 Boundary eigenvalue problems
34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Bxx Boundary value problems (For ordinary differential operators, see 34Lxx) / 34B24 Sturm-Liouville theory [See also 34Lxx]
34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Lxx Ordinary differential operators [See also 47E05] / 34L16 Numerical approximation of eigenvalues and of other parts of the spectrum
65-XX NUMERICAL ANALYSIS / 65Lxx Ordinary differential equations / 65L15 Eigenvalue problems
Collections:Universität Potsdam / Schriftenreihen / Preprints des Instituts für Mathematik der Universität Potsdam, ISSN 2193-6943 / 2012
Licence (German):License LogoKeine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht
Notes extern:RVK-Klassifikation: SI 990