Geodesic
Computational experiment for a class of mathematical models of magnetohydrodynamics
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 10 (2017) no. 1, pp. 149-155 Cet article a éte moissonné depuis la source Math-Net.Ru

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The first initial-boundary value problem for the system modelling the motion of the incompressible viscoelastic Kelvin–Voigt fluid in the magnetic field of the Earth is investigated considering that the fluid is under external influence. The problem is studied under the assumption that the fluid is under different external influences depending not only on the coordinates of the point in space but on time too. In the framework of the theory of semi-linear Sobolev type equations the theorem of existence and uniqueness of the solution of the stated problem is proved.The solution itself is a quasi-stationary semi-trajectory. The description of the problem's extended phase space is obtained.The results of the computainal experiment are presented.
Keywords: magnetohydrodynamics; Sobolev type equations; extended phase space; incompressible viscoelastic fluid; explicit one-step formulas of Runge–Kutta. 
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A. O. Kondyukov; T. G. Sukacheva; S. I. Kadchenko; L. S. Ryazanova. Computational experiment for a class of mathematical models of magnetohydrodynamics. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 10 (2017) no. 1, pp. 149-155. http://geodesic.mathdoc.fr/item/VYURU_2017_10_1_a9/

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[2] Sukacheva T. G., Kondyukov A. O., “Phase Space of a Model of Magnetohydrodynamics”, Differential Equations, 51:4 (2015), 502–509 | DOI | MR | Zbl

[3] Kadchenko S. I., Kondyukov A. O., “Numerical Study of a Flow of Viscoelastic Fluid of Kelvin–Voigt Having Zero Order in a Magnetic Field”, Journal of Computational and Engineering Mathematics, 3:2 (2016), 40–47 | DOI | MR | Zbl

[4] Sukacheva T. G., Kondyukov A. O., “On a Class of Sobolev Type Equations”, Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 7:4 (2014), 5–21 | DOI | Zbl

[5] Kondyukov A. O., Kadchenko S. I., Kakushkin S. N., Numerical Modelling of the Motion of the Viscoelastic Conductive Fluid in the Magnetic Field, The copyright holder: Federal state budgatary educational institution of higher education "Yaroslav-the-Wise Novgorod State University" (RU), No2016619268, registered 17.08.2016, the registry of computer programs