TY - INPR
A1 - Rattana, Amornrat
A1 - Böckmann, Christine
T1 - Matrix methods for computing Eigenvalues of Sturm-Liouville problems of order four
N2 - 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.
T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)13
KW - Finite difference method
KW - Numerov's method
KW - Boundary value methods
KW - Fourth order Sturm-Liouville problem
KW - Eigenvalues
Y1 - 2012
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-59279
ER -
TY - JOUR
A1 - Rattana, Amornrat
A1 - Böckmann, Christine
T1 - Matrix methods for computing eigenvalues of Sturm-Liouville problems of order four
JF - Journal of computational and applied mathematics
N2 - 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.
KW - Finite difference method
KW - Numerov's method
KW - Boundary value methods
KW - Fourth order Sturm-Liouville problem
KW - Eigenvalues
Y1 - 2013
U6 - https://doi.org/10.1016/j.cam.2013.02.024
SN - 0377-0427
SN - 1879-1778
VL - 249
IS - 8
SP - 144
EP - 156
PB - Elsevier
CY - Amsterdam
ER -