Математичне моделювання квадратично нелінійних просторово розподілених систем. І. Випадок дискретно визначених початково-крайових зовнішньодинамічних збурень / Стоян В. А. (2021)
Ukrainian

English  Cybernetics and Systems Analysis   /     Issue (2021, 57 (5))

Stoyan V.A.
Mathematical modeling of quadratically nonlinear spatially distributed systems. I. The case of discrete definite initial-boundary external-dynamic distubances

Two classes of nonlinear spatially distributed dynamical systems discretely observed according to the initial–boundary and spatially distributed external-dynamic perturbations are analyzed. For each of them, analytical dependences are constructed for the state function, which agrees, according to the root-mean square criterion, with the available information on external-dynamic conditions of their operation. Solution of the initial–boundary-value problems for the systems under study is defined in terms of a set of vectors, which, according to the root-mean-square criterion, model the given initial–boundary environment, including the spatially distributed external-dynamic perturbations. Conditions of the accuracy and uniqueness of the obtained mathematical results are presented. The cases of unbounded spatial domains and systems’ steady-state dynamics are considered. © 2021, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: ill-posed initial–boundary-value problems, mathematical modeling of dynamical systems, pseudo-solutions, spatially distributed dynamical systems, systems with uncertainties, Boundary value problems, Spatial distribution, Uncertainty analysis, External dynamics, Ill posed, Ill-posed initial–boundary-value problem, Initial-boundary value problems, Mathematical modeling of dynamical system, Pseudo solution, Root Mean Square, Spatially distributed dynamical systems, System with uncertainty, Uncertainty, Dynamical systems


Cite:
Stoyan V.A. (2021). Mathematical modeling of quadratically nonlinear spatially distributed systems. I. The case of discrete definite initial-boundary external-dynamic distubances. Cybernetics and Systems Analysis, 57 (5), 84–97. doi: https://doi.org/10.1007/s10559-021-00417-y http://jnas.nbuv.gov.ua/article/UJRN-0001268750 [In Ukrainian].


 

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