Extremal Eigenvalues of the Sturm-Liouville Problems with Discontinuous Coefficients

Extremal Eigenvalues of the Sturm-Liouville Problems with Discontinuous Coefficients

Year:    2013

Numerical Mathematics: Theory, Methods and Applications, Vol. 6 (2013), Iss. 4 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.2013.1208nm

Numerical Mathematics: Theory, Methods and Applications, Vol. 6 (2013), Iss. 4 : pp. 657–684

Published online:    2013-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    28

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

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