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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2011, Volume 51, Number 1, Pages 39–43 (Mi zvmmf8044)  

This article is cited in 20 scientific papers (total in 21 papers)

A modification of one method for solving nonlinear self-adjoint eigenvalue problems for hamiltonian systems of ordinary differential equations

A. A. Abramov

Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333 Russia
References:
Abstract: A modification of the method proposed earlier by the author for solving nonlinear selfadjoint eigenvalue problems for linear Hamiltonian systems of ordinary differential equations is examined. The basic assumption is that the initial data (that is, the system matrix and the matrices specifying the boundary conditions) are monotone functions of the spectral parameter.
Key words: Hamiltonian system of ordinary differential equations, nonlinear eigenvalue problem, eigenvalue.
Received: 01.06.2010
English version:
Computational Mathematics and Mathematical Physics, 2011, Volume 51, Issue 1, Pages 35–39
DOI: https://doi.org/10.1134/S0965542511010015
Bibliographic databases:
Document Type: Article
UDC: 519.626
Language: Russian
Citation: A. A. Abramov, “A modification of one method for solving nonlinear self-adjoint eigenvalue problems for hamiltonian systems of ordinary differential equations”, Zh. Vychisl. Mat. Mat. Fiz., 51:1 (2011), 39–43; Comput. Math. Math. Phys., 51:1 (2011), 35–39
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/zvmmf/v51/i1/p39
  • This publication is cited in the following 21 articles:
    1. Elyseeva J., Sepitka P., Hilscher R.S., “Oscillation Numbers For Continuous Lagrangian Paths and Maslov Index”, J. Dyn. Differ. Equ., 2022  crossref  isi
    2. Julia Elyseeva, A. Nadykto, N. Aleksic, P. Lima, P. Pivkin, L. Uvarova, X. Jiang, A. Zelensky, “The Oscillation Numbers and the Abramov Method of Spectral Counting for Linear Hamiltonian Systems”, EPJ Web Conf., 248 (2021), 01002  crossref
    3. Elyseeva J., “Comparison Theorems For Conjoined Bases of Linear Hamiltonian Systems Without Monotonicity”, Mon.heft. Math., 193:2 (2020), 305–328  crossref  isi
    4. Elyseeva J., “Oscillation Theorems For Linear Hamiltonian Systems With Nonlinear Dependence on the Spectral Parameter and the Comparative Index”, Appl. Math. Lett., 90 (2019), 15–22  crossref  mathscinet  isi
    5. Gavrikov A., “The Numerical Method For Solution of Eigenproblems For Linear Hamiltonian Systems and Its Application to the Eigenproblem For a Rotating Wedge Beam With a Crack”, AIP Conference Proceedings, 2116, eds. Simos T., Tsitouras C., Amer Inst Physics, 2019, 450074  crossref  isi
    6. Ondřej Došlý, Julia Elyseeva, Roman Šimon Hilscher, Pathways in Mathematics, Symplectic Difference Systems: Oscillation and Spectral Theory, 2019, 1  crossref
    7. Elyseeva J., “The Comparative Index and Transformations of Linear Hamiltonian Differential Systems”, Appl. Math. Comput., 330 (2018), 185–200  crossref  mathscinet  isi  scopus
    8. Elyseeva J., Hilscher R.S., “Discrete Oscillation Theorems For Symplectic Eigenvalue Problems With General Boundary Conditions Depending Nonlinearly on Spectral Parameter”, Linear Alg. Appl., 558 (2018), 108–145  crossref  mathscinet  zmath  isi  scopus
    9. A. A. Gavrikov, “Solution of eigenvalue problems for linear Hamiltonian systems with a nonlinear dependence on the spectral parameter”, Mech. Sol., 53:2 (2018), S118–S132  crossref  crossref  isi  elib  scopus
    10. A. A. Abramov, L. F. Yukhno, “Solving some problems for systems of linear ordinary differential equations with redundant conditions”, Comput. Math. Math. Phys., 57:8 (2017), 1277–1284  mathnet  crossref  crossref  isi  elib
    11. Gavrikov A., “Numerical Solution of Vector Sturm-Liouville Problems With a Nonlinear Dependence on the Spectral Parameter”, Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2016 (ICNAAM-2016), AIP Conference Proceedings, 1863, eds. Simos T., Tsitouras C., Amer Inst Physics, 2017, UNSP 560032-1  crossref  mathscinet  isi  scopus
    12. Abramov A.A., Yukhno L.F., “Nonlinear Spectral Problem For a Self-Adjoint Vector Differential Equation”, Differ. Equ., 53:7 (2017), 900–907  crossref  mathscinet  zmath  isi  scopus
    13. L. D. Akulenko, A. A. Gavrikov, S. V. Nesterov, “Numerical solution of vector Sturm–Liouville problems with Dirichlet conditions and nonlinear dependence on the spectral parameter”, Comput. Math. Math. Phys., 57:9 (2017), 1484–1497  mathnet  crossref  crossref  isi  elib  elib
    14. Gavrikov A.A., “Numerical Solution of Eigenproblems For Linear Hamiltonian Systems and Their Application to Non-Uniform Rod-Like Systems”, Proceedings of the International Conference Days on Diffraction (Dd) 2017, eds. Motygin O., Kiselev A., Goray L., Suslina T., Kazakov A., Kirpichnikova A., IEEE, 2017, 122–127  isi
    15. Alexander A. Gavrikov, 2017 Days on Diffraction (DD), 2017, 122  crossref
    16. E. D. Kalinin, “Solving the multiparameter eigenvalue problem for weakly coupled systems of second order Hamilton equations”, Comput. Math. Math. Phys., 55:1 (2015), 43–52  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    17. A. A. Abramov, L. F. Yukhno, “A nonlinear singular eigenvalue problem for a Hamiltonian system of differential equations with redundant condition”, Comput. Math. Math. Phys., 55:4 (2015), 597–606  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    18. Abramov A.A., Yukhno L.F., “Nonlinear Spectral Problem for a Hamiltonian System of Differential Equations with Redundant Conditions”, Differ. Equ., 50:7 (2014), 866–872  crossref  mathscinet  zmath  isi  elib  scopus
    19. Yu. V. Eliseeva, “An approach for computing eigenvalues of discrete symplectic boundary value problems”, Russian Math. (Iz. VUZ), 56:7 (2012), 47–51  mathnet  crossref  mathscinet
    20. M. K. Kerimov, “On the 85th birthday of Aleksandr Aleksandrovich Abramov”, Comput. Math. Math. Phys., 51:10 (2011), 1653–1658  mathnet  crossref  mathscinet  isi
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