scholarly journals Ordinary differential equations for the dynamic characteristics of heating boilers

2018 ◽  
Vol 194 ◽  
pp. 01024
Author(s):  
Sergei Khaustov ◽  
Olga Guk ◽  
Igor Razov
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Control Systems ◽  
Dynamic Characteristics ◽  
Solid Fuel ◽  
Computational Time ◽  
One Dimensional ◽  
Automatic Control Systems ◽  
Set Up

The paper presents ordinary differential equations for the dynamic characteristics of a solid fuel boiler that can be combined into one-dimensional nonstationary mathematical model for simulating long-term dynamics of a solid fuel boiler. This model requires less computational time for a qualitative simulation of boiler’s operation than known CFD-solutions. The long-term dynamic model presented can help to determine annual costs, to set up automatic control systems and to detect dangerous deviations in the project.

Normal form method in search for periodic solutions of ordinary differential equations. Case of the fourth order

2018 ◽  
pp. 24-34
Author(s):  
V. F. Edneral ◽  
O. D. Timofeevskaya
Keyword(s):  
Normal Form ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
Fourth Order ◽  
Numerical Solutions ◽  
Numerical Calculations ◽  
Computational Time ◽  
Resonant Normal Form ◽  
Normal Form Method

Introduction:The method of resonant normal form is based on reducing a system of nonlinear ordinary differential equations to a simpler form, easier to explore. Moreover, for a number of autonomous nonlinear problems, it is possible to obtain explicit formulas which approximate numerical calculations of families of their periodic solutions. Replacing numerical calculations with their precalculated formulas leads to significant savings in computational time. Similar calculations were made earlier, but their accuracy was insufficient, and their complexity was very high.Purpose:Application of the resonant normal form method and a software package developed for these purposes to fourth-order systems in order to increase the calculation speed.Results:It has been shown that with the help of a single algorithm it is possible to study equations of high orders (4th and higher). Comparing the tabulation of the obtained formulas with the numerical solutions of the corresponding equations shows good quantitative agreement. Moreover, the speed of calculation by prepared approximating formulas is orders of magnitude greater than the numerical calculation speed. The obtained approximations can also be successfully applied to unstable solutions. For example, in the Henon — Heyles system, periodic solutions are surrounded by chaotic solutions and, when numerically integrated, the algorithms are often unstable on them.Practical relevance:The developed approach can be used in the simulation of physical and biological systems.

COMPUTATIONAL APPROACH FOR ESTIMATING HYGRIC PROPERTIES OF HETEROGENEOUS MATERIALS IN LONG-TERM ASSESSMENT OF MOISTURE-INDUCED DAMAGE

2017 ◽  
Vol 4 (1) ◽  
Author(s):  
Václav Kočí ◽  
Jiří Maděra ◽  
Robert Černý
Keyword(s):  
Building Materials ◽  
Heterogeneous Materials ◽  
Computational Time ◽  
Computational Techniques ◽  
Computing Power ◽  
One Dimensional ◽  
Dimensional Modeling ◽  
Hygric Properties

Long-term assessment of degradation processes is a very useful tool for an analysis of building materials performance. Since computational techniques are mostly used for this purpose, hygric properties of involved materials are required as substantial input data. Unfortunately, some construction details or heterogeneous materials have to be solved by means of multi-dimensional modelling which is demanding on computing power and thus the calculations may take a lot of time. The presented paper aims at determination of effective hygric properties of heterogeneous materials which would allow one-dimensional transformation. The parameter identification process is carried out on the basis of results of multi-dimensional modeling, using genetic algorithms. The main objective is to find such effective global moisture transport and accumulation functions that provide in one-dimensional modeling as similar results to multidimensional modeling as possible. The obtained functions give a very good agreement; the investigated relative humidity profiles differ only by 1.48 percentage points in average. The correctness of obtained results is also verified using the Lichtenecker's mixing rule as homogenization technique. The transformation of the original multidimensional problem into one-dimensional is found to substantially contribute to minimization of computational time, which is reduced from weeks to minutes.

The Poincaré-Cartan forms of one-dimensional variational integrals

2020 ◽  
Vol 70 (6) ◽  
pp. 1381-1412
Author(s):  
Veronika Chrastinová ◽  
Václav Tryhuk
Keyword(s):  
Differential Equations ◽  
Variational Problem ◽  
Ordinary Differential Equations ◽  
Differential Forms ◽  
Point Of View ◽  
Full Generality ◽  
One Dimensional ◽  
Variational Integrals

AbstractFundamental concepts for variational integrals evaluated on the solutions of a system of ordinary differential equations are revised. The variations, stationarity, extremals and especially the Poincaré-Cartan differential forms are relieved of all additional structures and subject to the equivalences and symmetries in the widest possible sense. Theory of the classical Lagrange variational problem eventually appears in full generality. It is presented from the differential forms point of view and does not require any intricate geometry.

scholarly journals Qualitative behavior of stiff ODEs through a stochastic approach

2020 ◽  
Vol 10 (2) ◽  
pp. 181-187
Author(s):  
Hande Uslu ◽  
Murat Sari ◽  
Tahir Cosgun
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Real Life ◽  
Stochastic Approach ◽  
Computational Time ◽  
Qualitative Behavior ◽  
Computational Error ◽  
Linear Ordinary Differential Equations ◽  
Stiff Ordinary Differential Equations ◽  
Simulation Techniques

In the last few decades, stiff differential equations have attracted a great deal of interest from academic society, because much of the real life is covered by stiff behavior. In addition to importance of producing model equations, capturing an exact behavior of the problem by dealing with a solution method is also handling issue. Although there are many explicit and implicit numerical methods for solving them, those methods cannot be properly applied due to their computational time, computational error or effort spent for construction of a structure. Therefore, simulation techniques can be taken into account in capturing the stiff behavior. In this respect, this study aims at analyzing stiff processes through stochastic approaches. Thus, a Monte Carlo based algorithm has been presented for solving some stiff ordinary differential equations and system of stiff linear ordinary differential equations. The produced results have been qualitatively and quantitatively discussed.

Control Systems

2019 ◽  
pp. 31-40
Author(s):  
Pierre-Loïc Garoche
Keyword(s):  
Control System ◽  
Differential Equations ◽  
Control Theory ◽  
System Design ◽  
Ordinary Differential Equations ◽  
Control Systems ◽  
Control Design ◽  
Control System Design ◽  
Typical Development ◽  
Typical Process

This chapter sketches the typical development of control systems and refers the reader to classical books for more details on control system design. Historically, control design started in the continuous world: a system had to be controlled, and its dynamics was captured by the equations of physics, for example, using ordinary differential equations. Then, control theory provides means to build a controller: another system, used in combination with the system to be controlled, is able to move the system to the requested state. The chapter thus begins by presenting a typical process leading to the development of a controller in the aerospace domain. It then gives an idea of each step.

scholarly journals Quotients of Euler Equations on Space Curves

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 186
Author(s):  
Anna Duyunova ◽  
Valentin Lychagin ◽  
Sergey Tychkov
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Euler Equations ◽  
Gas Flow ◽  
Euler System ◽  
Partial Differential ◽  
One Dimensional ◽  
Space Curves ◽  
Ode System

Quotients of partial differential equations are discussed. The quotient equation for the Euler system describing a one-dimensional gas flow on a space curve is found. An example of using the quotient to solve the Euler system is given. Using virial expansion of the Planck potential, we reduce the quotient equation to a series of systems of ordinary differential equations (ODEs). Possible solutions of the ODE system are discussed.

scholarly journals Generalised Markovian control systems

1974 ◽  
Vol 18 (4) ◽  
pp. 485-491 ◽  
Author(s):  
P. E. Kloeden
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Control Systems ◽  
General Control ◽  
Qualitative Behaviour ◽  
Set Function

The qualitative behaviour of control systems based on ordinary differential equations has been investigated with clarity and elegance using axiomatically defined General Control Systems. Here an attainablity set function, evolving in semigroup fashion, is the main entity of interest [1], [2], [3], [4].

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