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Extremal Eigenvalues of the Sturm-Liouville Problems with Discontinuous Coefficients

Published online by Cambridge University Press:  28 May 2015

Shuangbing Guo*
Affiliation:
School of Mathematics and Statistics, Wuhan University, Wuhan 430072, Hubei, China
Dingfang Li*
Affiliation:
School of Mathematics and Statistics, Wuhan University, Wuhan 430072, Hubei, China
Hui Feng*
Affiliation:
School of Mathematics and Statistics, Wuhan University, Wuhan 430072, Hubei, China
Xiliang Lu*
Affiliation:
School of Mathematics and Statistics, Wuhan University, Wuhan 430072, Hubei, China
*
Corresponding author.Email address:iceflyingsouth@163.com
Corresponding author.Email address:dfli@whu.edu.en
Corresponding author.Email address:hui_fengl63@tom.com
Corresponding author.Email address:xllv.math@whu.edu.cn
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Abstract

In this paper, an extremal eigenvalue problem to the Sturm-Liouville equations with discontinuous coefficients and volume constraint is investigated. Liouville transformation is applied to change the problem into an equivalent minimization problem. Finite element method is proposed and the convergence for the finite element solution is established. A monotonic decreasing algorithm is presented to solve the extremal eigenvalue problem. A global convergence for the algorithm in the continuous case is proved. A few numerical results are given to depict the efficiency of the method.

Type
Research Article
Copyright
Copyright © Global Science Press Limited 2013

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