### ONMETHODSWITHSUCCESSIVEAPPROXIMATIONOF      THEINVERSEOPERATORFORNONLINEAREQUATIONSWITHDECOMPOSITIONOFTHEOPERATOR

Ioannis K. Argyros, Stepan Shakhno, Halyna Yarmola

#### Анотація

The problem of finding an approximate solution of a nonlinear equation with nondifferentiable operator is considered. For such a class of problems, it can be distinguished as a differentiable and nondifferentiable part in a nonlinear operator. New differential-difference methods, which contain the sum of the derivative of the differentiable part and the divided difference of the nondifferentiable part of the nonlinear operator, are developed. The proposed iterative process does not require finding the inverse operator. Instead of inverting the operator, its one- and two-step approximations are used. The study of local convergence of the methods under the Lipschitz condition for the divided differences of the first order and the restriction of the second derivative is carried out. The orders of convergence are established and the results of the numerical experiments are given.

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#### Посилання

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DOI: http://dx.doi.org/10.30970/vam.2020.28.10973

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