An inverse problem of chemical kinetics in a nondegenerate case

The article contains a review of recent results on solving the direct and inverse problems related to a singularly perturbed system of ordinary differential equations which describe a process in chemical kinetics. We also extend the class of problems under study by considering polynomials of arbitrary degree as the right-hand parts of the differential equations in the $\varepsilon \ne 0$. Moreover, an iteration algorithm is proposed of finding an approximate solution to the inverse problem in the nondegenerate $(\varepsilon \ne 0)$ for arbitrary degree. The theorem is proven on the convergence of the algorithm suggested. The proof is based on the contraction mapping principle (the Banach fixed-point theorem).