scholarly journals Numerical scheme for solving the nonuniformly forced cubic and quintic Swift-Hohenberg equations strictly respecting the Lyapunov functional

2021 ◽  
pp. 114005
Author(s):  
D.L. Coelho ◽  
E. Vitral ◽  
J. Pontes ◽  
N. Mangiavacchi
Keyword(s):  
Lyapunov Functional ◽  
Numerical Scheme

NUMERICAL SCHEME OF THE WAHA CODE

2008 ◽  
Vol 20 (3-4) ◽  
pp. 323-354 ◽  
Author(s):  
Iztok Tiselj ◽  
A. Horvat ◽  
J. Gale
Keyword(s):  
Numerical Scheme

PARALLEL SOLVER FOR THE SIMULATIONS OF DETONATION WAVES ON UNSTRUCTURED GRIDS

2020 ◽  
Author(s):  
A. I. Lopato ◽  
◽  
A. G. Eremenko ◽  
Keyword(s):  
Chemical Kinetics ◽  
Numerical Scheme ◽  
Unstructured Grids ◽  
Numerical Study ◽  
Numerical Approach ◽  
Detonation Waves ◽  
Detailed Chemical Kinetics ◽  
Parallel Solver ◽  
Further Development ◽  
Detailed Chemical

Recently, we developed a numerical approach for the simulation of detonation waves on fully unstructured grids and applied it to the numerical study of the mechanisms of detonation initiation in multifocusing systems. Current work is devoted to further development of our numerical approach, namely, parallelization of the numerical scheme and introduction of more comprehensive detailed chemical kinetics scheme.

Mathematical views of the fractional Chua's electrical circuit described by the Caputo-Liouville derivative

2021 ◽  
Vol 67 (1 Jan-Feb) ◽  
pp. 91
Author(s):  
N. Sene
Keyword(s):  
Caputo Derivative ◽  
Local Stability ◽  
Numerical Scheme ◽  
Equilibrium Points ◽  
Electrical Circuit ◽  
Maximal Lyapunov Exponent ◽  
Electrical Circuits ◽  
Adaptive Controls ◽  
Liouville Derivative

This paper revisits Chua's electrical circuit in the context of the Caputo derivative. We introduce the Caputo derivative into the modeling of the electrical circuit. The solutions of the new model are proposed using numerical discretizations. The discretizations use the numerical scheme of the Riemann-Liouville integral. We have determined the equilibrium points and study their local stability. The existence of the chaotic behaviors with the used fractional-order has been characterized by the determination of the maximal Lyapunov exponent value. The variations of the parameters of the model into the Chua's electrical circuit have been quantified using the bifurcation concept. We also propose adaptive controls under which the master and the slave fractional Chua's electrical circuits go in the same way. The graphical representations have supported all the main results of the paper.

Numerical Solution of a Nonlinear Diffusion Model for Soybean Hydration with Moving Boundary

2015 ◽  
Vol 11 (5) ◽  
pp. 587-595 ◽  
Author(s):  
Douglas J. Nicolin ◽  
Gisleine E. C. da Silva ◽  
Regina Maria M. Jorge ◽  
Luiz Mario M. Jorge
Keyword(s):  
Differential Equation ◽  
Diffusion Model ◽  
Nonlinear Diffusion ◽  
Numerical Scheme ◽  
Moving Boundary ◽  
Grid Method ◽  
Variable Diffusivity ◽  
Variable Space ◽  
Diffusive Fluxes ◽  
Moisture Profiles

Abstract Variable diffusivity and volume of the grains are taken into account in the diffusion model that describes mass transfer in soybean hydration. The variable space grid method (VSGM) was used to consider the increase in grain size, and the diffusivity was considered an exponential function of the moisture content. An equation for the behavior of the grain radius as a function of time was obtained by global mass balance over the soybean grain and the differential equation considered that the increase in radius happens due to the influence of the convective and diffusive fluxes at the surface of the grains. The model was solved by an explicit numerical scheme which presented satisfactory results. The results showed the behavior of moisture profiles obtained as a function of time and radial position and also showed how the grain radius increased with time and changed the solution domain of the diffusion equation.

Stabilization for a class of delayed switched inertial neural networks via non-reduced order method

2021 ◽  
pp. 014233122098594
Author(s):  
Xuan Chen ◽  
Dongyun Lin
Keyword(s):  
Neural Networks ◽  
Comparative Research ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Global Stabilization ◽  
Order Method ◽  
Reduced Order ◽  
Global Asymptotic Stabilization ◽  
Inertial Neural Networks ◽  
Barbalat Lemma

This paper tackles the issue of global stabilization for a class of delayed switched inertial neural networks (SINN). Distinct from the frequently employed reduced-order technique, this paper studies SINN directly through non-reduced order method. By constructing a novel Lyapunov functional and using Barbalat Lemma, sufficient conditions for the global asymptotic stabilization issue and global exponential stabilization issue of the considered SINN are established. Numerical simulations further confirm the feasibility of the main results. The comparative research shows that global stabilization results of this paper complement and improve some existing work.

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