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Mathematical Modeling of Spatially Distributed Systems Polynomially Dependent on Linear Differential Transformations of the State Function

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CYBERNETICS AND SYSTEMS ANALYSIS 2023年第2期59卷 296-305页

作者： Stoyan, V. A. Taras Shevchenko Natl Univ Kyiv Kiev Ukraine

The initial-boundary-value problems of the dynamics of nonlinear spatially distributed systems are formulated and solved using the root-mean-square criterion. Systems whose linear mathematical model is supplemented with the polynomially defined dependence on the differential transformation of their state function are considered. Analytical dependences of this function are generated in the presence of their discretely and continuously defined initial-boundary-value observations without constraints on the number and quality of the latter. The accuracy of the sets of obtained solutions is evaluated, and their uniqueness is analyzed.

关键词： nonlinear dynamical systems systems with uncertainties distributed-parameter systems spatially distributed systems pseudosolutions ill-posed initial-boundary-value problems

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Mathematical Modeling of Quadratically Nonlinear Spatially Distributed Systems. I. The Case of Discretely Defined initial-boundary External-Dynamic Perturbations

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CYBERNETICS AND SYSTEMS ANALYSIS 2021年第5期57卷 740-753页

作者： Stoyan, V. A. Taras Shevchenko Natl Univ Kyiv Kiev Ukraine

Two classes of nonlinear spatially distributed dynamical systems discretely observed according to the initial-boundary and spatially distributed external-dynamic disturbances 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.

关键词： pseudo-solutions mathematical modeling of dynamical systems spatially distributed dynamical systems systems with uncertainties ill-posed initial-boundary-value problems

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Mathematical Modeling of the State of Dynamical Multiplicatively Nonlinear Systems

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CYBERNETICS AND SYSTEMS ANALYSIS 2022年第4期58卷 598-610页

作者： Stoyan, V. A. Taras Shevchenko Natl Univ Kyiv Kiev Ukraine

The author formulates and solves, by the root-mean-square criterion, initial-boundary-value problems of the dynamics of nonlinear spatially distributed systems. Systems whose mathematical model is generated by the product of two or more differential transformations of their functions of state are considered. Analytical dependencies of this function are constructed in the presence of their discretely and continuously defined initial-boundary observations, without constraints for the number and quality of the latter. The accuracy of the sets of the obtained solutions is evaluated and their uniqueness is analyzed.

关键词： nonlinear dynamical systems systems with uncertainties distributed-parameter systems spatially distributed systems pseudosolutions ill-posed initial-boundary-value problems

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