Open AccessGeneralization of the Trotter–Daletsky formula for systems of the "reaction–diffusion" type
Author(s) -
V. М. Bondarenko,
А. А. Кравченко,
Tetiana Sobko
Publication year - 2021
Publication title -
sistemnì doslìdžennâ ta ìnformacìjnì tehnologìï
Language(s) - English
Resource type - Journals
eISSN - 2308-8893
pISSN - 1681-6048
DOI - 10.20535/srit.2308-8893.2021.4.08
Subject(s) - mathematics , semigroup , laplace operator , nonlinear system , ordinary differential equation , generalization , type (biology) , partial differential equation , cauchy problem , mathematical analysis , operator (biology) , cauchy distribution , perturbation (astronomy) , initial value problem , differential equation , physics , ecology , biochemistry , chemistry , repressor , quantum mechanics , gene , transcription factor , biology
An iterative method for constructing a solution to the Cauchy problem for a system of parabolic equations with a nonlinear potential has been proposed and substantiated. The method is based on the Trotter–Daletsky formula, generalized for a nonlinear perturbation of an elliptic operator. The idea of generalization is the construction of a composition of the semigroup generated by the Laplacian and the phase flow corresponding to a system of ordinary differential equations. A computational experiment performed for a two-dimensional system of semilinear parabolic equations of the “reaction–diffusion” type confirms estimates for the convergence of iterations established in the proof of this formula. Obtained results suggest the feasibility of an unconventional approach to modeling dynamic systems with distributed parameters.