scholarly journals Stability analysis of a system coupled to a heat equation

Automatica ◽  
2019 ◽  
Vol 99 ◽  
pp. 195-202 ◽  
Author(s):  
Lucie Baudouin ◽  
Alexandre Seuret ◽  
Frédéric Gouaisbaut
Keyword(s):  
Stability Analysis ◽  
Heat Equation

scholarly journals Stable Numerical Evaluation of Finite Hankel Transforms and Their Application

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Manoj P. Tripathi ◽  
B. P. Singh ◽  
Om P. Singh
Keyword(s):  
Stability Analysis ◽  
Heat Equation ◽  
Numerical Experiments ◽  
Numerical Evaluation ◽  
Radiation Condition ◽  
Hankel Transform ◽  
Basis Functions ◽  
Infinite Cylinder ◽  
Stable Algorithm ◽  
Hankel Transforms

A new stable algorithm, based on hat functions for numerical evaluation of Hankel transform of order ν>-1, is proposed in this paper. The hat basis functions are used as a basis to expand a part of the integrand, rf(r), appearing in the Hankel transform integral. This leads to a very simple, efficient, and stable algorithm for the numerical evaluation of Hankel transform. The novelty of our paper is that we give error and stability analysis of the algorithm and corroborate our theoretical findings by various numerical experiments. Finally, an application of the proposed algorithm is given for solving the heat equation in an infinite cylinder with a radiation condition.

scholarly journals A heat equation for freezing processes with phase change: stability analysis and applications

2015 ◽  
Vol 89 (4) ◽  
pp. 833-849 ◽  
Author(s):  
C. J. Backi ◽  
J. D. Bendtsen ◽  
J. Leth ◽  
J. T. Gravdahl
Keyword(s):  
Stability Analysis ◽  
Heat Equation ◽  
Phase Change

scholarly journals Stability theory for some scalar finite difference schemes: validity of the modified equations approach

2021 ◽  
Vol 70 ◽  
pp. 124-136
Author(s):  
Firas Dhaouadi ◽  
Emilie Duval ◽  
Sergey Tkachenko ◽  
Jean-Paul Vila
Keyword(s):  
Fourier Transform ◽  
Stability Analysis ◽  
Finite Difference ◽  
Heat Equation ◽  
Infinite Series ◽  
Stability Condition ◽  
Finite Difference Schemes ◽  
Modified Equations ◽  
The Stability ◽  
Modified Equation

In this paper, we discuss some limitations of the modified equations approach as a tool for stability analysis for a class of explicit linear schemes to scalar partial differential equations. We show that the infinite series obtained by Fourier transform of the modified equation is not always convergent and that in the case of divergence, it becomes unrelated to the scheme. Based on these results, we explain when the stability analysis of a given truncation of a modified equation may yield a reasonable estimation of a stability condition for the associated scheme. We illustrate our analysis by some examples of schemes namely for the heat equation and the transport equation.

scholarly journals Linear stability analysis and homoclinic orbit for a generalized non-linear heat transfer

2012 ◽  
Vol 16 (5) ◽  
pp. 1556-1559 ◽  
Author(s):  
Jun Liu ◽  
Xi Liu ◽  
Gui Mu ◽  
Litao Xie
Keyword(s):  
Heat Transfer ◽  
Stability Analysis ◽  
Heat Equation ◽  
Linear Stability ◽  
Dynamic Structure ◽  
Analytic Solutions ◽  
Linear Heat ◽  
Solitary Solutions ◽  
Non Linear ◽  
First Time

This paper studies the linear stability and dynamic structure for a generalized non-linear heat equation, and obtains novel analytic solutions such as homoclinc orbit and breather solitary solutions for the first time based on Hirota method.

Determination temperature of a backward heat equation with time-dependent coefficients

2012 ◽  
Vol 62 (5) ◽  
Author(s):  
Nguyen Tuan ◽  
Ngo Hoa
Keyword(s):  
Heat Conduction ◽  
Stability Analysis ◽  
Heat Equation ◽  
Error Estimates ◽  
Heat Conduction Problem ◽  
Time Dependent ◽  
Truncation Method ◽  
Regularization Parameters ◽  
The Stability

AbstractWe introduce the truncation method for solving a backward heat conduction problem with time-dependent coefficients. For this method, we give the stability analysis with new error estimates. Meanwhile, we investigate the roles of regularization parameters in these two methods. These estimates prove that our method is effective.

scholarly journals Influence of Quasiperiodic Gravitational Modulation on Convective Instability of Liquid-Liquid Polymerization Front

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Saadia Assiyad ◽  
Karam Allali ◽  
Mohamed Belhaq
Keyword(s):  
Stability Analysis ◽  
Heat Equation ◽  
Convective Instability ◽  
Stokes Equations ◽  
Boussinesq Approximation ◽  
Navier Stokes ◽  
Interface Problem ◽  
Navier Stokes Equations ◽  
Liquid Polymer ◽  
Concentration Equation

The influence of quasiperiodic gravitational modulation on convective instability of polymerization front with liquid monomer and liquid polymer is studied. The model includes the heat equation, the concentration equation, and the Navier-Stokes equations under the Boussinesq approximation. The linear stability analysis of the problem is carried out and the interface problem is derived. Using numerical simulations, the convective instability threshold is determined and the boundary of the convective instability is obtained for different amplitudes and frequencies ratio.

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