Approximation of the minimal eigenvalue for a nonlinear Sturm–Liouville problem

V. S. Zheltukhin   ; S. I. Solov'ev   ; P. S. Solov'ev

Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 157 (2015) no. 2, pp. 40-54

Résumé

Properties of the minimal eigenvalue corresponding to the positive eigenfunction of a nonlinear eigenvalue problem for an ordinary differential equation are studied. This problem is approximated by a mesh scheme of the finite element method. The error of approximate solutions is investigated. Theoretical results are illustrated by numerical experiments for a model eigenvalue problem.

Détail

Keywords: eigenvalue, positive eigenfunction, nonlinear eigenvalue problem, ordinary differential equation, finite element method.
Mots-clés : Sturm–Liouville problem

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