The identification problem for a nonsingular system of ordinary differential equations with fast and slow variables

An iteration algorithm of finding an approximate solution to an inverse problem in the nonsingular case ($\varepsilon$ = 0) is proposed. On each iteration step, the algorithm combines the inverse problem solution for the investigated case $\varepsilon$ = 0 and the direct problem solution which is reduced to the proof of existence and uniqueness theorem in case $\varepsilon$ = 0. We prove a theorem about the convergence of the proposed algorithm; the proof is based on the contraction mapping principle.