This article is cited in 5 papers

Numerical investigation of one Sobolev type mathematical model

A. A. Zamyshlyaeva, S. V. Surovtsev

South Ural State University, Chelyabinsk, Russian Federation

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.

UDC: 517.9

MSC: 65M06

Received: 20.08.2015

Language: English

DOI: 10.14529/jcem150308

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