Relationship between current response and time in ion transport problem including diffusion and convection. 2. Numerical approach

摘要

The mathematical model related to controlled potential experiments in electrochemistry is studied. Ion transport is regarded as the superposition of diffusion and migration under the influence of an electric field. Modeling of the experiment leads to the nonlocal identification problem for nonlinear parabolic equation. It is shown that in some cases the nonlocal identification problem can be transformed to an initial value problem for nonlinear parabolic equation. The finite diference approximation of this problem, with the appropriate iteration algorithm, is derived. Based on these algorithms the solution of the identification problem is presented. The obtained results permits one to derive the behaviour of the current response I_c(t){mathcal{I}}_c(t) , depending on time, also the relationship between the current response I_c(t){mathcal{I}}_c(t) and Gottrellian I_G{mathcal{I}}_G is obtained in explicit form. An influence of the valences oxidised and reduced species is also analyzed.