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Cybernetics And Systems Analysis
International Theoretical Science Journal
UDC 517.9: 519.6
V.M. Bulavatsky,1 V.O. Bohaienko2

NUMERICAL SIMULATION OF FRACTIONAL-DIFFERENTIAL FILTRATION-CONSOLIDATION
DYNAMICS WITHIN THE FRAMEWORK OF MODELS WITH NON-SINGULAR KERNEL

Abstract. Non-classical mathematical models to describe the fractional-differential filtration-consolidation dynamics of soil media saturated with saline solutions are constructed based on the concept of the fractional derivative of Caputo–Fabrizio. The corresponding boundary-value problems for the system of fractional- differential equations of filtration and salt transfer are posed, the technique for their numerical solution is developed, an approach to the parallelization of computations is presented and the results of numerical experiments on modeling the dynamics of the process are given.

Keywords: mathematical modeling, dynamics of filtration-consolidation processes, fractional-differential mathematical models, models with non-singular kernel, boundary-value problems, finite difference solutions, parallelization of computations.



FULL TEXT

1 V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine,
e-mail: v_bulav@ukr.net.

2 V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine,
e-mail: sevab@ukr.net.

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