«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2015. Vol. 12

Numerical Solution of the Linearized Oskolkov System

Author(s)
P. N. Davydov, M. V. Plekhanova
Abstract

Difference scheme is constructed for the numerical solution of the linearized Oskolkov model for Kelvin – Voigt fluid. The approximation of the scheme with the first order, stability and convergence has been proven. Problem-oriented programs complex is worked out for the numerical solution of the corresponding problem. Сomputing experiment was realized by means of the complex.

Keywords
Kelvin – Voight fluid, Oskolkov system of equations, numerical solution of initial boundary value problem, difference scheme stability, difference scheme convergence
UDC
517.9
References

1. Demidenko G.V., S.V. Upsenskii. Partial Differential Equations and Systems not Solvable with Respect to the Highest-Order Derivative. New York, Basel: Marcel Dekker, 2003.

2. Zvyagin, V. G., Turbin M. V. The study of initial-boundary value problems for mathematical models of the motion of Kelvin–Voigt fluids. Journal of Mathematical Sciences, 2010, vol. 168, № 2, pp.157–308.

3. Kalitkin N.N. CHislennye metody [Numerical methods]. SPb., BHV-Peterburg, 2011, 592 p. (in Russian)

4. Sveshnikov A. G., Al’shin A. B., Korpusov M. O., Pletner JU. D. Linejnye i nelinejnye uravnenija sobolevskogo tipa [Linear and Nonlinear Equations of Sobolev Type]. M., Fizmatlit, 2007, 734 р. (in Russian)

5. Oskolkov A.P. Initial-boundary value problems for equations of motion of Kelvin – Voight fluids and Oldroyd fluids. Proceedings of the Steklov Institute of Mathematics, 1989, vol. 179, pp. 137–182.

6. Svidetel’stvo o gosudarstvennoj registracii programmy dlja [Certificate of state registration of the computer number] JEVM № 2014618458 ROSPATENT/Davydov P.N., Plehanova M.V. zajavitel’ i pravoobladatel’ FGBOU VPO «Cheljabinskij gosudarstvennyj universitet». [the applicant and the right holder FGBOU VPO «Chelyabinsk State University».] № 2014616031 zajavlenie [Statement] 24.06.2014 gosudarstvennaja registracija v Reestre programm dlja JEVM [state registration in the Register of Computer Programs] 20.08.2014. (in Russian)

7. Fedorov V.E., Davydov P.N. Polulinejnye vyrozhdennye jevoljucionnye uravnenija i nelinejnye sistemy gidrodinamicheskogo tipa [Degenerate semilinear evolution equations and nonlinear systems of hydrodynamic type]. Trudy instituta matematiki i mehaniki UrO RAN. [Proceedings of the Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences], 2013, vol. 19, no 4, pp. 267–278. (in Russian)


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