• search hit 2 of 3
Back to Result List

## 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.

• Dokument_1.pdf Author: Amornrat Rattana, Christine BöckmannORCiDGND urn:nbn:de:kobv:517-opus-59279 Preprints des Instituts für Mathematik der Universität Potsdam (1(2012)13) Preprint English 2012 Universität Potsdam 2012/04/25 Boundary value methods; Eigenvalues; Finite difference method; Fourth order Sturm-Liouville problem; Numerov's method Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik 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 Universität Potsdam / Schriftenreihen / Preprints des Instituts für Mathematik der Universität Potsdam, ISSN 2193-6943 / 2012 Keine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht RVK-Klassifikation: SI 990