scholarly journals Analysis and Nonstandard Numerical Design of a Discrete Three-Dimensional Hepatitis B Epidemic Model

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1157 ◽  
Author(s):  
Jorge E. Macías-Díaz ◽  
Nauman Ahmed ◽  
Muhammad Rafiq
Keyword(s):  
Hepatitis B ◽  
Epidemic Model ◽  
Splitting Method ◽  
Three Dimensional ◽  
Reaction Diffusion ◽  
Superior Performance ◽  
Stability And Convergence ◽  
Dynamical Consistency ◽  
The Stability ◽  
The Mathematical Model

In this work, we numerically investigate a three-dimensional nonlinear reaction-diffusion susceptible-infected-recovered hepatitis B epidemic model. To that end, the stability and bifurcation analyses of the mathematical model are rigorously discussed using the Routh–Hurwitz condition. Numerically, an efficient structure-preserving nonstandard finite-difference time-splitting method is proposed to approximate the solutions of the hepatitis B model. The dynamical consistency of the splitting method is verified mathematically and graphically. Moreover, we perform a mathematical study of the stability of the proposed scheme. The properties of consistency, stability and convergence of our technique are thoroughly analyzed in this work. Some comparisons are provided against existing standard techniques in order to validate the efficacy of our scheme. Our computational results show a superior performance of the present approach when compared against existing methods available in the literature.

scholarly journals Stability and Bifurcation Analysis of a Modified Epidemic Model for Computer Viruses

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Chuandong Li ◽  
Wenfeng Hu ◽  
Tingwen Huang
Keyword(s):  
Hopf Bifurcation ◽  
Epidemic Model ◽  
Center Manifold ◽  
Dynamical Behavior ◽  
Three Dimensional ◽  
Normal Form Theory ◽  
Computer Viruses ◽  
Stability And Bifurcation ◽  
Form Theory ◽  
The Stability

We extend the three-dimensional SIR model to four-dimensional case and then analyze its dynamical behavior including stability and bifurcation. It is shown that the new model makes a significant improvement to the epidemic model for computer viruses, which is more reasonable than the most existing SIR models. Furthermore, we investigate the stability of the possible equilibrium point and the existence of the Hopf bifurcation with respect to the delay. By analyzing the associated characteristic equation, it is found that Hopf bifurcation occurs when the delay passes through a sequence of critical values. An analytical condition for determining the direction, stability, and other properties of bifurcating periodic solutions is obtained by using the normal form theory and center manifold argument. The obtained results may provide a theoretical foundation to understand the spread of computer viruses and then to minimize virus risks.

scholarly journals Numerical analysis of the stability of nonequilibrium 3D evolutionary transfer processes in the network

2021 ◽  
Vol 2094 (2) ◽  
pp. 022031
Author(s):  
V V Provotorov ◽  
A A Part ◽  
A V Shleenko ◽  
S M Sergeev
Keyword(s):  
Mathematical Model ◽  
Oil And Gas ◽  
Simulation Models ◽  
Original System ◽  
Time Variable ◽  
Stability And Convergence ◽  
Elliptic Type ◽  
Nonequilibrium Processes ◽  
The Stability ◽  
The Mathematical Model

Abstract Analytical methods for solving various problems of an applied nature (for example, non-stationary transfer problems over network hydro, gas and heat carriers), whose mathematical models use the formalisms of evolutionary differential systems, are possible with rare exceptions. That is why the construction of numerical and simulation models for the use of quantitative analysis methods becomes a universal research tool, if at the same time the implementation of these models on a computer is carried out – in other words, a complex of software engineering of the process under study is formed. The study uses the method of semidiscretization by a time variable of the mathematical model of the evolutionary non-equilibrium process of continuous medium transfer, which remains one of the most effective methods for analyzing applied problems. In this case, the elliptic operator of the mathematical model has a special basis (a system of eigenfunctions), which is why the analysis is reduced to the study of a boundary value problem for elliptic-type equations with a spatial variable changing on a network-like domain. The paper presents the conditions for unambiguous weak solvability of a differential-difference system, which is a difference analogue in the time variable of the original system, and the way of constructing an algorithm for finding an approximate solution is indicated. The study contains an analysis of the stability and convergence of difference schemes of evolutionary network-like nonequilibrium processes of continuous media transfer over network carriers and includes an analysis of the correctness of the mathematical model of this process. The results of the work are applicable in the framework of oil and gas engineering to the study of issues of stabilization and parametric optimization of the processes of transportation of liquid media through spatial networks.

scholarly journals An Efficient Hybrid Numerical Scheme for Nonlinear Multiterm Caputo Time and Riesz Space Fractional-Order Diffusion Equations with Delay

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
A. K. Omran ◽  
M. A. Zaky ◽  
A. S. Hendy ◽  
V. G. Pimenov
Keyword(s):  
Fractional Order ◽  
Reaction Diffusion ◽  
Riesz Space ◽  
Reaction Diffusion Equation ◽  
Stability And Convergence ◽  
Energy Estimates ◽  
Discrete Energy ◽  
Fully Discrete ◽  
Exponential Rate Of Convergence ◽  
The Stability

In this paper, we construct and analyze a linearized finite difference/Galerkin–Legendre spectral scheme for the nonlinear multiterm Caputo time fractional-order reaction-diffusion equation with time delay and Riesz space fractional derivatives. The temporal fractional orders in the considered model are taken as 0 < β 0 < β 1 < β 2 < ⋯ < β m < 1 . The problem is first approximated by the L 1 difference method on the temporal direction, and then, the Galerkin–Legendre spectral method is applied on the spatial discretization. Armed by an appropriate form of discrete fractional Grönwall inequalities, the stability and convergence of the fully discrete scheme are investigated by discrete energy estimates. We show that the proposed method is stable and has a convergent order of 2 − β m in time and an exponential rate of convergence in space. We finally provide some numerical experiments to show the efficacy of the theoretical results.

scholarly journals Numerical treatment of singularly perturbed delay reaction-diffusion equations

2020 ◽  
Vol 12 (1) ◽  
pp. 15-24
Author(s):  
Gashu Gadisa Kiltu ◽  
Gemechis File Duressa ◽  
Tesfaye Aga Bullo
Keyword(s):  
Time Delay ◽  
Present Method ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Singularly Perturbed ◽  
Diffusion Equations ◽  
Reaction Diffusion Equation ◽  
Stability And Convergence ◽  
Numerical Treatment ◽  
The Stability

This paper presents a uniform convergent numerical method for solving singularly perturbed delay reaction-diffusion equations. The stability and convergence analysis are investigated. Numerical results are tabulated and the effect of the layer on the solution is examined. In a nutshell, the present method improves the findings of some existing numerical methods reported in the literature. Keywords: Singularly perturbed, Time delay, Reaction-diffusion equation, Layer

scholarly journals Qualitative Simulation of the Growth of Electrolessly Deposited Cu Thin Films

2011 ◽  
Vol 2011 ◽  
pp. 1-13
Author(s):  
Hsiu-Chuan Wei
Keyword(s):  
Integrated Circuits ◽  
Diffusion Equation ◽  
Three Dimensional ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Processing Temperature ◽  
High Coverage ◽  
Growth Properties ◽  
Finite Difference Discretization ◽  
The Mathematical Model

Electroless deposition for fabricating copper (Cu) interconnects of integrated circuits has drawn attention due to its low processing temperature, high deposition selectivity, and high coverage. In this paper, three-dimensional computer simulations of the qualitative growth properties of Cu particles and two-dimensional simulations of the trench-filling properties are conducted. The mathematical model employed in the study is a reaction-diffusion equation. An implicit finite difference discretization with a red-black Gauss-Seidel method as a solver is proposed for solving the reaction-diffusion equation. The simulated deposition properties agree with those observed in experimentation. Alternatives to improve the deposition properties are also discussed.

The Stability and Convergence of Fully Discrete Galerkin-Galerkin FEMs for Porous Medium Flows

2014 ◽  
Vol 15 (4) ◽  
pp. 1141-1158 ◽  
Author(s):  
Buyang Li ◽  
Jilu Wang ◽  
Weiwei Sun
Keyword(s):  
Theoretical Analysis ◽  
Error Estimates ◽  
Three Dimensional ◽  
Time Discretization ◽  
Stability And Convergence ◽  
Time Step ◽  
Element Discretization ◽  
Flow Models ◽  
Fully Discrete ◽  
The Stability

AbstractThe paper is concerned with the unconditional stability and error estimates of fully discrete Galerkin-Galerkin FEMs for the equations of incompressible miscible flows in porous media. We prove that the optimal L2 error estimates hold without any time-step (convergence) conditions, while all previous works require certain time-step restrictions. Theoretical analysis is based on a splitting of the error into two parts: the error from the time discretization of the PDEs and the error from the finite element discretization of the corresponding time-discrete PDEs, which was proposed in our previous work [26, 27]. Numerical results for both two and three-dimensional flow models are presented to confirm our theoretical analysis.

scholarly journals On stability and bifurcation of solutions of an SEIR epidemic model with vertical transmission

2004 ◽  
Vol 2004 (56) ◽  
pp. 2971-2987 ◽  
Author(s):  
M. M. A. El-Sheikh ◽  
S. A. A. El-Marouf
Keyword(s):  
Hopf Bifurcation ◽  
Global Stability ◽  
Vertical Transmission ◽  
Epidemic Model ◽  
Center Manifold ◽  
Three Dimensional ◽  
Stability And Bifurcation ◽  
The Stability ◽  
Bifurcation Of Solutions

A four-dimensional SEIR epidemic model is considered. The stability of the equilibria is established. Hopf bifurcation and center manifold theories are applied for a reduced three-dimensional epidemic model. The boundedness, dissipativity, persistence, global stability, and Hopf-Andronov-Poincaré bifurcation for the four-dimensional epidemic model are studied.

Analysis on Influence of Dynamic Setting AGC Model Parameters on the Stability of Control System

2010 ◽  
Vol 145 ◽  
pp. 128-133
Author(s):  
Chun Jiang Zhao ◽  
Lian Yun Jiang ◽  
Jin Zhi Zhang ◽  
Qing Xue Huang ◽  
Xiao Kai Yu
Keyword(s):  
Mathematical Model ◽  
Control System ◽  
Convergence Rate ◽  
Mathematical Analysis ◽  
Stability And Convergence ◽  
Model Parameters ◽  
Recursive Methods ◽  
Dynamic Setting ◽  
The Stability ◽  
The Mathematical Model

Based on the theory of mathematical analysis, I find the rolling disturbance can be measured. Then the mathematical model of dynamic setting AGC is gotten by recursive methods. By the mathematical model I find out the influence of model parameters on the stability and convergence rate of the control system. When the system is stable, an influence of model parameters and parameter of the control system on steel strap thickness have been obtained, which will be helpful for us to choose suitable parameters in the end.

scholarly journals STABILITY ANALYSIS OF SEIDEL TYPE MULTICOMPONENT ITERATIVE METHOD

2002 ◽  
Vol 7 (1) ◽  
pp. 1-10
Author(s):  
V. N. Abrashin ◽  
R. Čiegis ◽  
V. Pakeniene ◽  
N. G. Zhadaeva
Keyword(s):  
Stability Analysis ◽  
Iterative Method ◽  
Iterative Methods ◽  
Convergence Rates ◽  
Splitting Method ◽  
Three Dimensional ◽  
Initial Approximation ◽  
Discrete Problem ◽  
Smooth Functions ◽  
The Stability

This paper deals with the stability analysis of multicomponent iterative methods for solving elliptic problems. They are based on a general splitting method, which decomposes a multidimensional parabolic problem into a system of one dimensional implicit problems. Error estimates in the L 2 norm are proved for the first method. For the stability analysis of Seidel type iterative method we use a spectral method. Two dimensional and three dimensional problems are investigated. Finally, we present results of numerical experiments. Our goal is to investigate the dependence of convergence rates of multicomponent iterative methods on the smoothness of the solution. Hence we solve a discrete problem, which approximates the 3D Poisson's problem. It is proved that the number of iterations depends weakly on the number of grid points if the exact solution and the initial approximation are smooth functions, both. The same problem is also solved by the Stability Correction iterative method. The obtained results indicate a similar behavior.

scholarly journals TESTING THE CACTUS CODE ON EXACT SOLUTIONS OF THE EINSTEIN FIELD EQUATIONS

2002 ◽  
Vol 13 (06) ◽  
pp. 805-821 ◽  
Author(s):  
DUMITRU N. VULCANOV ◽  
MIGUEL ALCUBIERRE
Keyword(s):  
Exact Solutions ◽  
Numerical Simulations ◽  
Three Dimensional ◽  
Einstein Equations ◽  
Stability And Convergence ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Modern Cosmology ◽  
The Stability ◽  
The Universe

The article presents a series of numerical simulations of exact solutions of the Einstein equations performed using the Cactus code, a complete three-dimensional machinery for numerical relativity. We describe an application ("thorn") for the Cactus code that can be used for evolving a variety of exact solutions, with and without matter, including solutions used in modern cosmology for modeling the early stages of the universe. Our main purpose has been to test the Cactus code on these well-known examples, focusing mainly on the stability and convergence of the code.

Sign in / Sign up

Export Citation Format

Share Document