Numerical solution of a nonlocal identification problem for nonlinear ion transport

A numerical method for the solution of a parameter identification problem in a nonlinear non-self-adjoint two-point boundary value problem with an additional nonlocal condition defining the parameter is presented. The equation arises in the modelling of an experiment known as chronoamperometry for the study of kinetics and mass-transfer in electrochemical events. The algorithm is based on the reformulation of the identification problem as a nonlinear fixed-point problem involving the concentration flux of the reduced species. The linearized boundary value problem is shown to have a unique solution with the unknown parameter uniquely determined by the flux. The linearized BVP is solved using finite differences and the fixed-point is found using the α-bisection method. The results of computational experiments are presented and their physical significance is discussed.