An inverse problem in estimating the reaction functions and solute concentration simultaneously in a reversible process

An inverse algorithm basing on the Iterative Regularization Method (IRM) is applied in this study in determining the unknown time-dependent reaction functions and solute concentration in the solution, i.e. three unknown time-dependent functions, simultaneously in a reversible process by using measurements of concentration components. It is assumed that no prior information is available on the functional form of the unknown functions in the present study, it can thus be classified as function estimation for the inverse calculations. The accuracy of this inverse problem is examined by using the simulated exact and inexact concentration measurements in the numerical experiments. Results show that the estimation of the time-dependent reaction functions and solute concentration in the solution can be obtained in a very short CPU time on a HP d2000 2.66 GHz personal computer. Moreover, the sensors should be placed as close to the boundary as possible to obtain better estimations.