5733 2012 eng preprint 1 2012-04-25 -- -- 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. urn:nbn:de:kobv:517-opus-59279 5927 RVK-Klassifikation: SI 990 Keine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht Amornrat Rattana Christine Böckmann Preprints des Instituts für Mathematik der Universität Potsdam 1(2012)13 eng uncontrolled Finite difference method eng uncontrolled Numerov's method eng uncontrolled Boundary value methods eng uncontrolled Fourth order Sturm-Liouville problem eng uncontrolled Eigenvalues Mathematik Boundary eigenvalue problems Sturm-Liouville theory [See also 34Lxx] Numerical approximation of eigenvalues and of other parts of the spectrum Eigenvalue problems open_access 2012 Institut für Mathematik Universität Potsdam https://publishup.uni-potsdam.de/files/5733/premath13.pdf 34797 2013 2013 eng 144 156 13 8 249 article Elsevier Amsterdam 1 -- -- -- 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 methods 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 is 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. Journal of computational and applied mathematics 10.1016/j.cam.2013.02.024 0377-0427 1879-1778 wos:2011-2013 WOS:000318133500013 Rattana, A (reprint author), Univ Potsdam, Inst Math, Neuen Palais 10, D-14469 Potsdam, Germany., karattana@hotmail.com; bockmann@rz.uni-potsdam.de Amornrat Rattana Christine Böckmann eng uncontrolled Finite difference method eng uncontrolled Numerov's method eng uncontrolled Boundary value methods eng uncontrolled Fourth order Sturm-Liouville problem eng uncontrolled Eigenvalues Institut für Mathematik Referiert 34054 2013 2013 eng 121 S. doctoralthesis Potsdam 1 -- -- -- Direct and inverse sturm-liouville problems of order four allegro:1991-2014 10111176 Potsdam, Univ., Diss., 2013 Amornrat Rattana Institut für Mathematik