Geodesic
Finding of a numerical solution to the Cauchy--Dirichlet problem for Boussinesq--L\`ove equation using finite differences method
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 6 (2015), pp. 76-81

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The article is devoted to the numerical investigation of Boussinesq–Lòve mathematical model. Algorithm for finding numerical solution to the Cauchy–Dirichlet problem for Boussinesq–Lòve equation modeling longitudinal oscillations in a thin elastic rod with regard to transverse inertia was obtained on the basis of phase space method and by using finite differences method. This problem can be reduced to the Cauchy problem for Sobolev type equation of the second order, which is not solvable for arbitrary initial values. The constructed algorithm includes 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.
Mots-clés : Boussinesq–Lòve equation, Sobolev type equation, Thomas algorithm.
Keywords: Cauchy–Dirichlet problem, finite differences method, phase space, conditions of data consistency, system of difference equations 
@article{VSGU_2015_6_a8,
     author = {A. A. Zamyshlyaeva and S. V. Surovtsev},
     title = {Finding of a numerical solution to the {Cauchy--Dirichlet} problem for {Boussinesq--L\`ove} equation using finite differences method},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {76--81},
     publisher = {mathdoc},
     number = {6},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2015_6_a8/}
}
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A. A. Zamyshlyaeva; S. V. Surovtsev. Finding of a numerical solution to the Cauchy--Dirichlet problem for Boussinesq--L\`ove equation using finite differences method. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 6 (2015), pp. 76-81. http://geodesic.mathdoc.fr/item/VSGU_2015_6_a8/