Stoyan V.A.
Mathematical modeling of spatially distributed systems, polynomially dependent on linear differential transformations of the state function

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. © 2023, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: distributed-parameter systems, ill-posed initial–boundary-value problems, nonlinear dynamical systems, pseudosolutions, spatially distributed systems, systems with uncertainties, Boundary value problems, Dynamical systems, Linear transformations, Spatial distribution, Uncertainty analysis, Differential transformation, Distributed parameter systems, Ill posed, Ill-posed initial–boundary-value problem, Initial-boundary value problems, Pseudosolution, Spatially-distributed system, State functions, System with uncertainty, Uncertainty, Nonlinear dynamical systems

Cite:
Stoyan V.A. (2023). Mathematical modeling of spatially distributed systems, polynomially dependent on linear differential transformations of the state function. Cybernetics and Systems Analysis, 59 (2), 136–145. doi: https://doi.org/10.1007/s10559-023-00563-5 http://jnas.nbuv.gov.ua/article/UJRN-0001392163 [In Ukrainian].