Computer modeling of the dynamics of migration processes of soluble substances in the case of groundwater filtration with free surface on the base of the fractional derivative approach

1Bogaenko, VA
1Bulavatsky, VM
1V.M. Glushkov Institute of Cybernetics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2018, 12:21-29
https://doi.org/10.15407/dopovidi2018.12.021
Section: Information Science and Cybernetics
Language: Russian
Abstract: 

The mathematical modeling of the fractional differential dynamics of the process of anomalous convective diffusion of soluble substances is conducted for the case of flat-vertical steady state groundwater filtration with free surface. Within the framework of the model with a generalized Caputo—Gerasimov fractional derivative, the corresponding non-linear boundary-value problem is posed, a finite-difference method for its approximated solution is given, and the results of computer experiments are described.

Keywords: dynamics of convective and diffusive processes, finite-difference solutions, fractional differential mathematical models, generalized Caputo—Gerasimov derivative, mathematical and computer modeling, non-linear boundary-value problems, steady state flat-vertical groundwater filtration
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