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
Urheberrechtsschutz
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