Abstract
In this paper a class of Boundary Value Methods obtained as an extension of the Numerov's method is proposed for the numerical approximation of the eigenvalues of regular Sturm-Liouville problems subject to Dirichlet boundary conditions. It is proved that the error in the so obtained estimate of the kth eigenvalue behaves as O (kp + 1 hp - frac(1, 2)) + O (kp + 2 hp), where p is the order of accuracy of the method and h is the discretization stepsize. Numerical results comparing the performances of the new matrix methods with that of the corrected Numerov's method are also reported.
Original language | English |
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Pages (from-to) | 1644-1656 |
Number of pages | 13 |
Journal | Applied Numerical Mathematics |
Volume | 59 |
Issue number | 7 |
DOIs | |
Publication status | Published - Jul 2009 |
Externally published | Yes |
Keywords
- Boundary Value Methods
- Eigenvalues
- Sturm-Liouville problems