Balgaisha Mukanova, Natalya Glazyrina , Sergey Glazyrin
Nonlinear inverse problem for a model of ion-exchange filter: numerical recovery of parameters
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ABSTRACT. In the article considers the problem of calculating the impurities concentration for an ion-exchange filter model. The model consists of the material balance equation, the equation of the kinetics of ion exchange for the nonequilibrium case and of the ion exchange isotherm. In the material balance equation there is a nonlinear term depending on the kinetics of ion exchange. A numerical solution of the direct problem of calculating the impurities concentration at the outlet of the filter is provided. The inverse problem is formulated as refers to finding the parameters of a mathematical model of an ion-exchange process in non-equilibrium conditions. A method for determining the effective values of that parameters is developed based on measurements of the impurities concentration at the outlet of the filter. The method is used to solve the inverse problem of recovering one and two unknown parameters of the ion-exchange filter model.