Boundary Value Methods as an extension of Numerov's method for Sturm-Liouville eigenvalue estimates

被引：21
作者：
Aceto, L. [1 ]
Ghelardoni, P. [1 ]
Magherini, C. [1 ]
机构：
[1] Univ Pisa, Dipartimento Matemat Applicata U Dini, I-56127 Pisa, Italy
来源：
APPLIED NUMERICAL MATHEMATICS | 2009年 / 59卷 / 07期
关键词：
Boundary Value Methods; Sturm-Liouville problems; Eigenvalues; ASYMPTOTIC CORRECTION; SPECTRAL CORRECTIONS; APPROXIMATIONS; COMPUTATION; MATRICES; EQUATION;
D O I：
10.1016/j.apnum.2008.11.005
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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(k(p+1)h(p-1/2)) + O(k(p+2)h(p)), 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. (C) 2008 IMACS. Published by Elsevier B.V. All rights reserved.
引用
收藏
页码：1644 / 1656
页数：13
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