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.
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
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\by A.~A.~Abramov
\paper A~modification of one method for solving nonlinear self-adjoint eigenvalue problems for hamiltonian systems of ordinary differential equations
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2011
\vol 51
\issue 1
\pages 39--43
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\jour Comput. Math. Math. Phys.
\yr 2011
\vol 51
\issue 1
\pages 35--39
\crossref{https://doi.org/10.1134/S0965542511010015}
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Linking options:
https://www.mathnet.ru/eng/zvmmf8044
https://www.mathnet.ru/eng/zvmmf/v51/i1/p39
This publication is cited in the following 21 articles:
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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
Elyseeva J., “Comparison Theorems For Conjoined Bases of Linear Hamiltonian Systems Without Monotonicity”, Mon.heft. Math., 193:2 (2020), 305–328
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
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
Ondřej Došlý, Julia Elyseeva, Roman Šimon Hilscher, Pathways in Mathematics, Symplectic Difference Systems: Oscillation and Spectral Theory, 2019, 1
Elyseeva J., “The Comparative Index and Transformations of Linear Hamiltonian Differential Systems”, Appl. Math. Comput., 330 (2018), 185–200
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
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
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
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
Abramov A.A., Yukhno L.F., “Nonlinear Spectral Problem For a Self-Adjoint Vector Differential Equation”, Differ. Equ., 53:7 (2017), 900–907
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
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
Alexander A. Gavrikov, 2017 Days on Diffraction (DD), 2017, 122
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
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
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
Yu. V. Eliseeva, “An approach for computing eigenvalues of discrete symplectic boundary value problems”, Russian Math. (Iz. VUZ), 56:7 (2012), 47–51
M. K. Kerimov, “On the 85th birthday of Aleksandr Aleksandrovich Abramov”, Comput. Math. Math. Phys., 51:10 (2011), 1653–1658