TY - JOUR
T1 - Extremal Eigenvalues of the Sturm-Liouville Problems with Discontinuous Coefficients
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 - <p style="text-align: justify;">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.</p>