Approximation of the Minimal Eigenvalue for a Nonlinear Sturm–Liouville Problem
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. Theore...
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| Format: | Article |
| Language: | English |
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Kazan Federal University
2015-06-01
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| Series: | Учёные записки Казанского университета. Серия Физико-математические науки |
| Subjects: | |
| Online Access: | https://kpfu.ru/portal/docs/F1793906104/157_2_phys_mat_4.pdf |
| _version_ | 1797859142343327744 |
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| author | V.S. Zheltukhin S.I. Solov’ev P.S. Solov’ev |
| author_facet | V.S. Zheltukhin S.I. Solov’ev P.S. Solov’ev |
| author_sort | V.S. Zheltukhin |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-09T21:24:43Z |
| format | Article |
| id | doaj.art-45d2cbba197444b987ac1ee993d7d7b2 |
| institution | Directory Open Access Journal |
| issn | 2541-7746 2500-2198 |
| language | English |
| last_indexed | 2024-04-09T21:24:43Z |
| publishDate | 2015-06-01 |
| publisher | Kazan Federal University |
| record_format | Article |
| series | Учёные записки Казанского университета. Серия Физико-математические науки |
| spelling | doaj.art-45d2cbba197444b987ac1ee993d7d7b22023-03-27T16:38:20ZengKazan Federal UniversityУчёные записки Казанского университета. Серия Физико-математические науки2541-77462500-21982015-06-0115724054Approximation of the Minimal Eigenvalue for a Nonlinear Sturm–Liouville ProblemV.S. Zheltukhin0S.I. Solov’ev1P.S. Solov’ev2Kazan National Research Technological University, Kazan, 420015 RussiaKazan Federal University, Kazan, 420008 RussiaKazan Federal University, Kazan, 420008 RussiaProperties 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.https://kpfu.ru/portal/docs/F1793906104/157_2_phys_mat_4.pdfeigenvaluepositive eigenfunctionnonlinear eigenvalue problemordinary differential equationsturm–liouville problemfinite element method |
| spellingShingle | V.S. Zheltukhin S.I. Solov’ev P.S. Solov’ev Approximation of the Minimal Eigenvalue for a Nonlinear Sturm–Liouville Problem Учёные записки Казанского университета. Серия Физико-математические науки eigenvalue positive eigenfunction nonlinear eigenvalue problem ordinary differential equation sturm–liouville problem finite element method |
| title | Approximation of the Minimal Eigenvalue for a Nonlinear Sturm–Liouville Problem |
| title_full | Approximation of the Minimal Eigenvalue for a Nonlinear Sturm–Liouville Problem |
| title_fullStr | Approximation of the Minimal Eigenvalue for a Nonlinear Sturm–Liouville Problem |
| title_full_unstemmed | Approximation of the Minimal Eigenvalue for a Nonlinear Sturm–Liouville Problem |
| title_short | Approximation of the Minimal Eigenvalue for a Nonlinear Sturm–Liouville Problem |
| title_sort | approximation of the minimal eigenvalue for a nonlinear sturm liouville problem |
| topic | eigenvalue positive eigenfunction nonlinear eigenvalue problem ordinary differential equation sturm–liouville problem finite element method |
| url | https://kpfu.ru/portal/docs/F1793906104/157_2_phys_mat_4.pdf |
| work_keys_str_mv | AT vszheltukhin approximationoftheminimaleigenvalueforanonlinearsturmliouvilleproblem AT sisolovev approximationoftheminimaleigenvalueforanonlinearsturmliouvilleproblem AT pssolovev approximationoftheminimaleigenvalueforanonlinearsturmliouvilleproblem |