Geodesic
Convergence of some iterative algorithms for numerical solution of two-dimensional non-stationary problems of magnetic hydrodynamics
Matematičeskoe modelirovanie, Tome 35 (2023) no. 2, pp. 57-74.

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The work studies the convergence of methods of combined and separate solution of difference equations groups, divided by physical processes, applied to a family of completely conservative difference schemes (CCDS) of two-dimensional magnetohydrodynamics (MHD). Estimates are obtained for the convergence of iterative processes for the entire family of CCDS both for the method of separate and combined solution of groups of difference equations. These results are obtained for the first time; previously, such estimates were obtained only for a purely implicit difference scheme. The validity of the estimates obtained in the work is confirmed by numerical calculations. Based on the estimates obtained in this work, recommendations were developed for any CCDS, which numerical method is more appropriate to use to solve the system of difference equations. Depending on the ratio of the parameters of the substance and the electromagnetic field at each moment of time, the estimates obtained in this work, even for calculating one physical problem of two-dimensional MHD, make it possible to choose the optimal numerical method for each time integration step, which leads to a significant reduction in the computational time of the problem. This can be quite important, especially when conducting a large-scale computational experiment. Thus, the results obtained in this work have not only interesting theoretical, but also important practical significance.
Keywords: two-dimensional magnetohydrodynamics, family of completely conservative difference schemes, convergence of iterative process. 
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A. Yu. Krukovskiy; Yu. A. Poveshchenko; V. O. Podryga. Convergence of some iterative algorithms for numerical solution of two-dimensional non-stationary problems of magnetic hydrodynamics. Matematičeskoe modelirovanie, Tome 35 (2023) no. 2, pp. 57-74. http://geodesic.mathdoc.fr/item/MM_2023_35_2_a4/

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