Finite Element Approximation of the Minimal Eigenvalue and the Corresponding Positive Eigenfunction of a Nonlinear Sturm—Liouville Problem
| Autor: | D. M. Korosteleva, P. S. Solov’ev, S. I. Solov’ev |
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| Rok vydání: | 2019 |
| Předmět: |
General Mathematics
010102 general mathematics Mathematical analysis Sturm–Liouville theory Mathematics::Spectral Theory Eigenfunction 01 natural sciences Finite element method 010305 fluids & plasmas Nonlinear system Ordinary differential equation 0103 physical sciences Order (group theory) 0101 mathematics Differential (mathematics) Eigenvalues and eigenvectors Mathematics |
| Zdroj: | Lobachevskii Journal of Mathematics. 40:1959-1966 |
| ISSN: | 1818-9962 1995-0802 |
| DOI: | 10.1134/s1995080219110179 |
| Popis: | The problem of finding the minimal eigenvalue and the corresponding positive eigenfunction of the nonlinear Sturm—Liouville problem for the ordinary differential equation with coefficients nonlinear depending on a spectral parameter is investigated. This problem arises in modeling the plasma of radio-frequency discharge at reduced pressures. A sufficient condition for the existence of a minimal eigenvalue and the corresponding positive eigenfunction of the nonlinear Sturm— Liouville problem is established. The original differential eigenvalue problem is approximated by the finite element method with Lagrangian finite elements of arbitrary order on a uniform grid. The error estimates of the approximate eigenvalue and the approximate positive eigenfunction to exact ones are proved. Investigations of this paper generalize well known results for the Sturm—Liouville problem with linear entrance on the spectral parameter. |
| Databáze: | OpenAIRE |
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