Geodesic
Numerical solving unsteady problems for the system of the Nernst--Planck equations
Matematičeskoe modelirovanie, Tome 24 (2012) no. 10, pp. 133-148.

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The mathematical model of electricity and mass transfer processes is based on the governing equations for the concentration of charged particles (ions and cations) in an electrolyte — the Nernst–Planck equations. These equations are supplemented with the equation for the electric field and the equations for a motion of electrolyte as a continuum medium. In this work we have focused on constructing approximations in time for approximate solving unsteady problems. The system of the Nernst-Planck equations is characterized by a quadratic non-linearity. To take info accont this nonlinearity, we propose special schemes of linearization. Computational algorithms are studied using a model problem for a binary electrolyte (two types of charged particles).
Keywords: electricity and mass transfer, the Nernst–Planck equations, difference scheme, quadratic non-inearity. 
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P. N. Vabishchevich; O. P. Iliev. Numerical solving unsteady problems for the system of the Nernst--Planck equations. Matematičeskoe modelirovanie, Tome 24 (2012) no. 10, pp. 133-148. http://geodesic.mathdoc.fr/item/MM_2012_24_10_a10/

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