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Numerical Simulation of Distributed Devices for the Processing of UltraWideband Information Read chapter Read first chapter

2021 | OriginalPaper | Chapter

Research of the Boundary Value Problem for the Sophie Germain Equationinin in a Cyber-Physical System

Author : Andrey Ushakov

Published in: Cyber-Physical Systems: Modelling and Intelligent Control

Publisher: Springer International Publishing

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Abstract

We consider the boundary value problem for an inhomogeneous biharmonic equation and extend the problem in a variational form. Also, we carry out the discretization of the considered problem by the finite element method. The continued problems, is presented in matrix form. An iterative process is formulated for an approximate solution to the original problem. The problem in matrix form is solved by method of fictitious components. Estimates of the convergence of the iterative process are given. Research of the problem being solved is reduced to a cyber-physical system. The estimates of the convergence of the absolute error do not depend on the grid steps. An algorithm is formulated for solving the investigated computer problem. To process information in the algorithm, a variation method is used. The steepest descent method is used to control computations in the iterative process. The software implementation of the algorithm uses certain elements of artificial intelligence.

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previous chapter Numerical Approaches to Solving a Non-linear System of Schrödinger Equations
next chapter Modeling of Vibration Separation of Bulk Materials Based on the Theory of Random Processes
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Metadata
Title
Research of the Boundary Value Problem for the Sophie Germain Equationinin in a Cyber-Physical System
Author
Andrey Ushakov
Copyright Year
2021
Book
Cyber-Physical Systems: Modelling and Intelligent Control

Print ISBN: 978-3-030-66076-5

Electronic ISBN: 978-3-030-66077-2

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-3-030-66077-2_5

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