Numerical Inversion for Determining Time-Dependent Reaction Coefficient in 1-D Solute Transportation by Homotopy Regularization Algorithm

This paper deals with an inverse problem for determining a time-dependent reaction coefficient in one-dimensional advection-dispersion equation by the homotopy regularization algorithm. Numerical inversions are carried out by choosing homotopy parameters with two different methods respectively, and inversion results are also presented by utilizing an optimal perturbation regularization algorithm to compare with those of homotopy methods. Impacts of regularization parameters and initial iterations on the inversion algorithms are discussed which show that the homotopy regularization algorithm is more efficient than the optimal perturbation algorithm at least for the inverse problem here.