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Volume 6, Issue 4
Extremal Eigenvalues of the Sturm-Liouville Problems with Discontinuous Coefficients

Shuangbing Guo, Dingfang Li, Hui Feng & Xiliang Lu

DOI: 10.4208/nmtma.2013.1208nm

Numer. Math. Theor. Meth. Appl., 6 (2013), pp. 657-684.

Published online: 2013-06

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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.

  • Keywords

Extremal eigenvalue problem, Sturm-Liouville problem, finite element method, convergence analysis.

  • AMS Subject Headings

65L60, 65L15, 34B09

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-6-657, author = {Shuangbing Guo, Dingfang Li, Hui Feng and Xiliang Lu}, title = {Extremal Eigenvalues of the Sturm-Liouville Problems with Discontinuous Coefficients}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2013}, volume = {6}, number = {4}, pages = {657--684}, 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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2013.1208nm}, url = {http://global-sci.org/intro/article_detail/nmtma/5924.html} }
TY - JOUR T1 - Extremal Eigenvalues of the Sturm-Liouville Problems with Discontinuous Coefficients AU - Shuangbing Guo, Dingfang Li, Hui Feng & Xiliang Lu JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 657 EP - 684 PY - 2013 DA - 2013/06 SN - 6 DO - http://doi.org/10.4208/nmtma.2013.1208nm UR - https://global-sci.org/intro/article_detail/nmtma/5924.html KW - Extremal eigenvalue problem, Sturm-Liouville problem, finite element method, convergence analysis. AB -

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.

Shuangbing Guo, Dingfang Li, Hui Feng and Xiliang Lu. (2013). Extremal Eigenvalues of the Sturm-Liouville Problems with Discontinuous Coefficients. Numerical Mathematics: Theory, Methods and Applications. 6 (4). 657-684. doi:10.4208/nmtma.2013.1208nm
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