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Numerical solution of vector Sturm–Liouville problems with Dirichlet conditions and nonlinear dependence on the spectral parameter

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Abstract

A numerical-analytical iterative method is proposed for solving generalized self-adjoint regular vector Sturm–Liouville problems with Dirichlet boundary conditions. The method is based on eigenvalue (spectral) correction. The matrix coefficients of the equations are assumed to be nonlinear functions of the spectral parameter. For a relatively close initial approximation, the method is shown to have second-order convergence with respect to a small parameter. Test examples are considered, and the model problem of transverse vibrations of a hinged rod with a variable cross section is solved taking into account its rotational inertia.

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology, Dolgoprudnyi, Moscow oblast, 141701, Russia

    L. D. Akulenko

  2. Bauman Moscow State Technical University, Moscow, 105005, Russia

    L. D. Akulenko

  3. Institute for Problems of Mechanics, Russian Academy of Sciences, Moscow, 119526, Russia

    L. D. Akulenko, A. A. Gavrikov & S. V. Nesterov

Authors
  1. L. D. Akulenko
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  2. A. A. Gavrikov
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  3. S. V. Nesterov
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Correspondence to L. D. Akulenko.

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Original Russian Text © L.D. Akulenko, A.A. Gavrikov, S.V. Nesterov, 2017, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2017, Vol. 57, No. 9, pp. 1503–1516.

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Akulenko, L.D., Gavrikov, A.A. & Nesterov, S.V. Numerical solution of vector Sturm–Liouville problems with Dirichlet conditions and nonlinear dependence on the spectral parameter. Comput. Math. and Math. Phys. 57, 1484–1497 (2017). https://doi.org/10.1134/S0965542517090020

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  • DOI: https://doi.org/10.1134/S0965542517090020

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