UDC 519.6
MATHEMATICAL MODELING OF QUADRATICALLY NONLINEAR
SPATIALLY DISTRIBUTED SYSTEMS.
I. THE CASE OF DISCRETE DEFINITE INITIAL-BOUNDARY
EXTERNAL-DYNAMIC DISTUBANCES
Abstract. Two classes of nonlinear spatially distributed dynamic 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 initialboundary-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 disturbances. Conditions of the accuracy and uniqueness of the obtained mathematical results are presented.
The cases of unrestricted spatial domains and systems’ stable dynamics are considered.
Keywords: pseudo-solutions, mathematical modeling of dynamical systems, spatially distributed dynamical systems, systems with non-definitions, incorrect initial-boundary problems.
FULL TEXT
REFERENCES
- Lavrent'ev M.M., Romanov V.G., Shishatsky S.P. Ill-posed problems of mathematical physics and analysis [in Russian]. Moscow: Nauka, 1980. 288 p.
- Ivanov V.K., Vasin V.V., Tanana V.P. The theory of linear ill-posed problems and its applications [in Russian]. Moscow: Nauka, 1978. 206 p.
- Kirichenko N.F. Pseudo-inversion of matrices and their recurrence in problems of modeling and control. Problemy upravleniya i informatiki. 1995. N 1. P. 114–127.
- Kirichenko N.F., Stoyan V.A. Analytical representation of matrix and integral linear transformations. Kibernetika i sistemnyj analiz. 1998. N 3. P. 90-104.
- Stoyan V.A. On one approach to the analysis of initial-boundary value problems in mathematical physics. Problemy upravleniya i informatiki. 1998. N 1. P. 79–86.
- Stoyan V.A. Mathematical modeling of the dynamics of incompletely observed linear spatially distributed systems. Kiev: IPC "Kiev University", 2019. 318 p.
- Stoyan V.A. Mathematical modeling of linear, quasi-dynamic and non-dynamic dynamical systems [in Russian]. Kiev: IPC “Kiev University”, 2011. 320 p.
- Stoyan V.A., Dvirnychuk V.B. Towards constructing the integral equivalent of linear differential models. Dop. NAS of Ukraine. 2012. N 9. P. 36–43.
- Methods of linear algebra in problems of the analysis of certain classes of nonlinear discretely transformative systems. I. Multiplicatively nonlinear systems. Kibernetika i sistemnyj analiz. 2019. Vol. 55, N 1. P. 127–134.
- Linear algebra methods in problems of the analysis of certain classes of nonlinear discretely transformative systems. II. Systems with additionally highlighted nonlinearity. Kibernetika i sistemnyj analiz. 2019. Vol. 55, N 2. P. 102–107.
- Stoyan V.A. To the construction of integral mathematical models of two classes of nonlinear spatially distributed systems. І. The case of discretely defined external dynamic disturbances. Kibernetika i sistemnyj analiz. 2019. Vol. 55, N 5. P. 115–127.
- Stoyan V.A. To the construction of integral mathematical models of two classes of nonlinear spatially distributed systems. II. The case of continuously defined external dynamic perturbations. Kibernetika i sistemnyj analiz. 2020. Vol. 56, N 1. P. 118–127.
- Bulavatsky V.M., Kryvonos Iu.G., Skopetsky V.V. Non-classical mathematical models of heat and mass transfer processes [in Ukrainian]. Kyiv: Nauk. opinion, 2005. 282 p.
- Bomb A.Ya., Bulavatsky V.M., Skopetsky V.V. Nonlinear mathematical models of geohydrodynamic processes [in Ukrainian]. Kyiv: Nauk. dumka, 2007. 291 p.
