scholarly journals Note on the Sensitivity of Simulated Solutions of the Nonlinear Singularly Perturbed Dynamical System on the Used Different Rewriting into a System of First Order Differential Equations

2016 ◽  
Vol 24 (39) ◽  
pp. 51-55
Author(s):  
Vladimír Liška ◽  
Zuzana Šútova ◽  
Dušan Pavliak
Keyword(s):  
Dynamical System ◽  
Numerical Methods ◽  
Differential Equations ◽  
Numerical Simulations ◽  
Numerical Scheme ◽  
Singularly Perturbed ◽  
First Order ◽  
First Order Differential Equations

Abstract In this paper we analyze the sensitivity of solutions to a nonlinear singularly perturbed dynamical system based on different rewriting into a System of the First Order Differential Equations to a numerical scheme. Numerical simulations of the solutions use numerical methods implemented in MATLAB.

Dynamics of Temperatures in Thermally-Coupled, Heated Rooms With PI Control

2007 ◽  
Author(s):  
Frederick W. Thwaites ◽  
Mihir Sen
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Coupled System ◽  
Time Dependent ◽  
Pi Control ◽  
Thermal Coupling ◽  
First Order ◽  
Dependent Behavior ◽  
The Stability ◽  
First Order Differential Equations

The purpose of this study is to analyze the behavior of a set of thermally-controlled rooms arranged in the form of a ring. Each room is heated and can exchange heat with its neighbors as well as with the environment. The heater in each room is PI controlled. A lumped capacitance approximation is used for the rooms leading to a system of first-order differential equations. Numerical methods are used to determine the time-dependent behavior of the coupled system. The linear stability of the system is analyzed for various parameters. The stability is found to be independent of the strength of the thermal coupling between rooms.

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