Abstract
In this paper, an extremal eigenvalue problem to the Sturm-Liouville equa- tions with discontinuous coefficients and volume constraint is investigated. Liouville transformation is applied to change the problem into an equivalent minimization prob- lem. Finite element method is proposed and the convergence for the finite element solution is established. A monotonic decreasing algorithm is presented to solve the ex- tremal 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. AMS subject classifications: 65L60, 65L15, 34B09
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