treated similarly).

Assume that (\[noneq\]) is solvable (not necessarily uniquely). If the Fréchet derivative of the operator $F$ has nontrivial null-space at the solution to (\[noneq\]), then one can use the classical Newton method for solution to (\[noneq\]) only under some strong assumptions on the operator $F$ (see [@dkk; @ag]). Otherwise in order to construct a numerical method for solution to (\[noneq\]) one needs some regularization procedure.

In the theory of ill-posed problems many different discrete methods based on a regularization are known. Many different convergence theorems for such schemes describe the efficiency of the numerical algorithms for solving various nonlinear problems, and give existence results (see, for example, [@bns; @ehn; @va]). However it is quite difficult to navigate in the sea of the discrete schemes and corresponding convergence theorems. Proofs of these theorems are usually based on the contraction mapping principle and are sometimes rather complicated.

On the other hand an analysis of continuous processes is based on the investigation of the asymptotical behavior of nonlinear dynamical systems in Banach and Hilbert spaces. If a convergence theorem is proved for a continuous method, one can construct various discrete schemes generated by this continuous process. Thus construction of a discrete 