ASYMPTOTIC OF SOLVING A DYNAMIC PROBLEM OF ELASTICITY THEORY FOR AN INCOMPRESSIBLE MEDIUM

Koikelova D.K. Bukenov M.M. Kankenova A.M. Muratkhan R. Serikbayeva A.B.
30 May 2022 Little Lion Scientific

Journal of Theoretical and Applied Information Technology
2022 #100 Issue 8 2687 - 2695 pp.

In this paper, the behavior of the solution of the dynamic problem and the theory of elasticity as λ → ∞ for the second boundary value problem is studied. An unimprovable estimate of the rate of convergence of the solution for a compressible medium to an incompressible parameter 1/ λ is obtained. In [1], the following question was considered, approximations of the solution of the problem for an incompressible medium by the solution of the problem for compressible media as λ → ∞, as well as the possibility justification for using the difference schemes proposed in [2] to obtain a solution to the problem under study. In [3,4], the dynamic problem of contact of compressible and incompressible media was considered, theorems on the existence and uniqueness of a generalized solution were proved, and estimates were obtained for the proximity of the solution of a contact problem to solutions of problems for compressible and incompressible media. In this paper, we have studied the stability of the difference scheme proposed by A.N. Kanavalov for solving the dynamic problem of elasticity theory. The approximation analysis allows to select the optimal grid steps associated with the parameter λ.

Deformations , Displacements , E Task Of The Stokes , Incompressible Medium , Theory Of Elasticity

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L.N.Gumilyov Eurasian National University, Department of Mathematical and Computer Modeling, Nur-Sultan, Kazakhstan
Karaganda Buketov University, Department of Applied Mathematics and Informatics, Karagandy, Kazakhstan
Master of Technical Sciences, S.Seifullin Kazakh Agro Technical University, Department of Information Systems, Nur-Sultan, Kazakhstan

L.N.Gumilyov Eurasian National University
Karaganda Buketov University
Master of Technical Sciences

10 лет помогаем публиковать статьи Международный издатель

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