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.
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References
V. A. Stoyan, Mathematical Modeling of Linear, Quasilinear, and Nonlinear Dynamical Systems [in Ukrainian], VPTs “Kyiv. Univ.,” Kyiv (2011).
V. A. Stoyan, “Mathematical modeling of quadratically nonlinear spatially distributed systems. I. The case of discretely defined initial–boundary external-dynamic perturbations,” Cybern. Syst. Analysis, Vol. 57, No. 5, 740–753 (2021). https://doi.org/10.1007/s10559-021-00399-x.
V. A. Stoyan, “Mathematical modeling of quadratically nonlinear spatially distributed systems. II. The case of continuously defined initial–boundary external-dynamic perturbations,” Cybern. Syst. Analysis, Vol. 57, No. 6, 906–917 (2021). https://doi.org/10.1007/s10559-021-00417-y.
V. A. Stoyan, “Mathematical modeling of the state of dynamical multiplicatively nonlinear systems,” Cybern. Syst. Analysis, Vol. 58, No. 4, 598–610 (2022). https://doi.org/10.1007/s10559-022-00493-8.
I. V. Sergienko, V. V. Skopetsky, and V. S. Deineka, Mathematical Modeling and Analysis of Processes in Heterogeneous Media [in Russian], Naukova Dumka, Kyiv (1991).
V. M. Bulavatsky, Iu. G. Kryvonos, and V. V. Skopetsky, Nonclassical Mathematical Models of Heat and Mass Transfer Processes [in Ukrainian], Naukova Dumka, Kyiv (2005).
V. A. Stoyan, “An approach to the analysis of initial–boundary-value problems of mathematical physics,” Problemy Upravl. Inform., No. 1, 79–86 (1998).
V. A. Stoyan, “Pseudoinversion of the mathematical models of distributed differential systems with additive definite nonlinearity,” Cybern. Syst. Analysis, Vol. 57, No. 1, 66–81 (2021). https://doi.org/10.1007/s10559-021-00330-4.
N. F. Kirichenko and V. A. Stoyan, “Analytical representations of matrix and integral linear transformations,” Cybern. Syst. Analysis, Vol. 34, No. 3, 395–408 (1998). https://doi.org/10.1007/BF02666981.
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Translated from Kibernetyka ta Systemnyi Analiz, No. 2, March–April, 2023, pp. 136–145.
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Stoyan, V.A. Mathematical Modeling of Spatially Distributed Systems Polynomially Dependent on Linear Differential Transformations of the State Function. Cybern Syst Anal 59, 296–305 (2023). https://doi.org/10.1007/s10559-023-00563-5
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DOI: https://doi.org/10.1007/s10559-023-00563-5