Extremal Eigenvalues of the Sturm-Liouville Problems with Discontinuous Coefficients
Shuangbing Guo, Dingfang Li, Hui Ze Feng, Xiliang Lu · Numerical Mathematics Theory Methods and Applications · 2013
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