Abstract: In this paper, Discrete Newton Method for solving nonlinear operator equations and Tikhonov's regularization method for solving linear ill-posed problems are combined into a stable iterative scheme for solving nonlinear operator equations with hard computed and ill-conditioned derivatives. The results of convergence analyses and error estimates are ob-tained. The application of this method for solving the inverse problem on remote sensing of the thermal conductivity in the nonhomogeneous material is demonstrated. It is shown by numerical simulations that this method is feasible and effective.

Key words: nonlinear system of equations, regularization method, inverse problem of differential equation