Abstract:
The article is devoted to a numerical investigation of the Boussinesq – Love mathematical model. Algorithm for finding of the numerical solution to the Cauchy – Dirichlet problem for the Boussinesq – Love equation modeling longitudinal oscillations in a thin elastic rod with regard to transverse inertia was obtained on the basis of a phase space method and by using a finite differences method. This problem can be reduced to the Cauchy problem for the Sobolev type equation of the second order, which is not solvable for arbitrary initial values. The constructed algorithm includes the additional check if initial data belongs to the phase space. The algorithm is implemented as a program in Matlab. The results of numerical experiments are obtained both in regular and degenerate cases. The graphs of obtained solutions are presented in each case.
Keywords:
Boussinesq – Love equation, Cauchy – Dirichlet problem, finite differences method, Sobolev type equation, phase space, conditions of data consistency, system of difference equations, the Thomas algorithm.
Citation:
A. A. Zamyshlyaeva, S. V. Surovtsev, “Numerical investigation of one Sobolev type mathematical model”, J. Comp. Eng. Math., 2:3 (2015), 72–80
\Bibitem{ZamSur15}
\by A.~A.~Zamyshlyaeva, S.~V.~Surovtsev
\paper Numerical investigation of one Sobolev type mathematical model
\jour J. Comp. Eng. Math.
\yr 2015
\vol 2
\issue 3
\pages 72--80
\mathnet{http://mi.mathnet.ru/jcem23}
\crossref{https://doi.org/10.14529/jcem150308}
\elib{https://elibrary.ru/item.asp?id=24505469}
Linking options:
https://www.mathnet.ru/eng/jcem23
https://www.mathnet.ru/eng/jcem/v2/i3/p72
This publication is cited in the following 5 articles:
Mohamed Jleli, Bessem Samet, “Instantaneous blow-up for a Sobolev-type equation arising in the theory of propagation of nonlinear waves in semiconductors”, DCDS-S, 2025
Mohamed Jleli, B. Samet, Praveen Agarwal, “Instantaneous Blow‐Up for a Generalized Drift Wave Differential Inequality of Sobolev Type”, Math Methods in App Sciences, 2025
Mohamed Jleli, Bessem Samet, “On the critical behavior for a Sobolev-type inequality with Hardy potential”, Comptes Rendus. Mathématique, 362:G1 (2024), 87
Bessem Samet, “Instantaneous blow-up for a semiconductor-type equation posed in an infinite cylinder”, DCDS-S, 2024
E. V. Bychkov, “Finite difference method for modified Boussinesq equation”, J. Comp. Eng. Math., 5:4 (2018), 58–63
Citation in format AMSBIB
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