Open AccessDifferential-difference method with approximation of the inverse operator
Author(s) -
Stepan Shakhno,
Halyna Yarmola
Publication year - 2021
Publication title -
fìziko-matematične modelûvannâ ta ìnformacìjnì tehnologìï/fìzìko-matematične modelûvannâ ta ìnformacìjnì tehnologìï
Language(s) - English
Resource type - Journals
eISSN - 2617-5258
pISSN - 1816-1545
DOI - 10.15407/fmmit2021.33.186
Subject(s) - mathematics , lipschitz continuity , differentiable function , operator (biology) , bounded function , semi elliptic operator , differential operator , inverse , nonlinear system , mathematical analysis , convergence (economics) , biochemistry , chemistry , physics , geometry , repressor , quantum mechanics , transcription factor , economics , gene , economic growth
The problem of finding an approximate solution of a nonlinear equation with operator decomposition is considered. For equations of this type, a nonlinear operator can be represented as the sum of two operators – differentiable and nondifferentiable. For numerical solving such an equation, a differential-difference method, which contains the sum of the derivative of the differentiable part and the divided difference of the nondifferentiable part of the nonlinear operator, is proposed. Also, the proposed iterative process does not require finding the inverse operator. Instead of inverting the operator, its one-step approximation is used. The analysis of the local convergence of the method under the Lipschitz condition for the first-order divided differences and the bounded second derivative is carried out and the order of convergence is established.