Узагальнення формули Троттера–Далецького для систем типу "реакція–дифузія"
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...
Збережено в:
| Дата: | 2021 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | rus |
| Опубліковано: |
The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute"
2021
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| Теми: | |
| Онлайн доступ: | http://journal.iasa.kpi.ua/article/view/252318 |
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| Назва журналу: | System research and information technologies |
Репозитарії
System research and information technologies| Резюме: | 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. |
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