Vestnik Samarskogo universiteta. Estestvennonauchnaya seriya / Vestnik of Samara University. Natural Science SeriesVestnik Samarskogo universiteta. Estestvennonauchnaya seriya / Vestnik of Samara University. Natural Science Series2541-75252712-8954Samara National Research University447010.18287/2541-7525-2015-21-6-76-81Finding of a numerical solution tothe Cauchy - Dirichlet problem for Boussinesq - Lo`ve equation using ﬁnitediﬀerences methodZamyshlyaevaA.A.morenov.sv@ssau.ruSurovtsevS.V.morenov.sv@ssau.ruSouth Ural State University1706201521676811705201717052017Copyright © 2015, Zamyshlyaeva A., Surovtsev S.2015The article is devoted to the numerical investigation of Boussinesq - L`ove mathematical model. Algorithm for ﬁnding numerical solution to the Cauchy - Dirichlet problem for Boussinesq - Lo`ve 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.уравнение Буссинеска — Лява, задача Коши — Дирихле, метод конечных разностей, уравнение соболевского типа, фазовое пространство, условия согласования, система разностных уравнений, метод прогонки.Boussinesq – L`ove equation, Cauchy – Dirichlet problem, finite differences method, Sobolev type equation, phase space, conditions of data consistency, system of difference equations, Thomas algorithm