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.
Author details: | Amornrat Rattana, Christine BöckmannORCiDGND |
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DOI: | https://doi.org/10.1016/j.cam.2013.02.024 |
ISSN: | 0377-0427 |
ISSN: | 1879-1778 |
Title of parent work (English): | Journal of computational and applied mathematics |
Publisher: | Elsevier |
Place of publishing: | Amsterdam |
Publication type: | Article |
Language: | English |
Year of first publication: | 2013 |
Publication year: | 2013 |
Release date: | 2017/03/26 |
Tag: | Boundary value methods; Eigenvalues; Finite difference method; Fourth order Sturm-Liouville problem; Numerov's method |
Volume: | 249 |
Issue: | 8 |
Number of pages: | 13 |
First page: | 144 |
Last Page: | 156 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
Peer review: | Referiert |