Abstract. The authors construct a mathematical model to describe the dynamics of fractional-differential locally nonequilibrium in time convection-diffusion process of soluble substances in the plain-vertical steady-state filtration with a free boundary. The statement of the respective boundary-value problem is presented and the technique of obtaining its approximated solution is set up. Developed parallel algorithms of calculation for cluster systems, the results of testing of response parallel algorithms for the GPU and results of numerical experiments on simulation of dynamics of considered migration process are adduced
Keywords: non-classical diffusion models, non-equilibrium in times convective-diffusion process, plainly-vertical filtration in porous medium, diffusion equation with delay, fractional diffusion equation, boundary value problems, approximated solutions, parallel algorithms.
Булавацкий Владимир Михайлович,
доктор техн. наук, профессор, ведущий научный сотрудник Института кибернетики им. В.М. Глушкова НАН Украины, Киев,
e-mail: v_bulav@ukr.net.
Богаенко Всеволод Анатольевич,
кандидат техн. наук, старший научный сотрудник Института кибернетики им. В.М. Глушкова НАН Украины, Киев,
e-mail: sevab@ukr.net.