Збіжність ітерацій у формулі Троттера–Далецького для нелінійного збурення - Bondarenko, Viktor G.; Markevych, Ihor S. (The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", 2019)
An iterative method for constructing a solution to the Cauchy problem for a parabolic equation with a nonlinear potential ("reaction–diffusion" type equation) is proposed and substantiated. The method is based on the Trotter–Daletsky formula that is generalized for a nonlinear perturbation of an elliptic operator. The essence of the generalization is the composition of the semigroup of an elliptic generator and the phase flow generated by an ordinary differential equation. The estimates of the rate of convergence of iterations established in the proof of this formula were confirmed by the computational experiment performed for the Kolmogorov–Petrovsky–Piskunov–Fisher equation. The obtained results suggest the feasibility of an unconventional approach to the modeling of dynamic systems with distributed parameters. A model of the space-time dynamics of the water community in terms of the two-species "predator–prey" system was shown as an example.