Open AccessFinding of a numerical solution tothe Cauchy - Dirichlet problem for Boussinesq - Lo`ve equation using finitedifferences method
Author(s) -
A.A. Zamyshlyaeva,
S. V. Surovtsev
Publication year - 2015
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2015-21-6-76-81
Subject(s) - mathematics , initial value problem , cauchy problem , degenerate energy levels , dirichlet problem , mathematical analysis , cauchy distribution , dirichlet distribution , sobolev space , physics , boundary value problem , quantum mechanics
The article is devoted to the numerical investigation of Boussinesq - L`ove mathematical model. Algorithm for nding 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 nite dierences 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.