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Stochastic SEIR epidemic models with virus mutation and logistic growth of susceptible populations

Mathematics and Computers in simulation 2023年第1期212卷 289-309页

作者： Wang, Qi Xiang, Kainan Zhu, Chunhui Zou, Lang Hunan Key Laboratory for Computation and Simulation in Science and Engineering & Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education & School of Mathematics and Computational Science Xiangtan University Hunan Province Xiangtan City411105 China National Center for Applied Mathematics in Hunan China

This article introduces a kind of stochastic SEIR models containing virus mutation and logistic growth of susceptible populations, whose deterministic versions have a positively invariant set and globally asymptotically stable equilibrium points. For these stochastic SEIR epidemic models, we prove they have a unique global positive solution, and also obtain sufficient conditions respectively for survival and extinction of the infectious disease. Eventually, we validate our theoretical findings using numerical simulations. © 2023 International Association for Mathematics and Computers in simulation (IMACS)

关键词： Viruses

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AN EFFICIENT MOVING MESH METHOD FOR A MODEL OF TURBULENT FLOW IN CIRCULAR TUBES

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Journal of computational Mathematics 2009年第2期27卷 388-399页

作者： Yin Yang Yanping Chen Yunqing Huang Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Xiangtan 411105 China School of Mathematical Sciences South China Normal University Guangzhou China

This paper presents an efficient moving problem with an optimal control constrained mesh method to solve a nonlinear singular condition. The physical problem is governed by a new model of turbulent flow in circular tubes proposed by Luo et al. using Prandtl＇s mixing-length theory. Our algorithm is formed by an outer iterative algorithm for handling the optimal control condition and an inner adaptive mesh redistribution algorithm for solving the singular governing equations. We discretize the nonlinear problem by using a upwinding approach, and the resulting nonlinear equations are solved by using the Newton- Raphson method. The mesh is generated and the grid points are moved by using the arc-length equidistribution principle. The numerical results demonstrate that proposed algorithm is effective in capturing the boundary layers associated with the turbulent model.

关键词： Eddy viscosity Turbulent pipe flow Boundary layer Optimal control Moving mesh

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Legendre Neural Network for Solving Linear Variable Coefficients Delay Differential-Algebraic Equations with Weak Discontinuities

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Advances in Applied Mathematics and Mechanics 2021年第1期13卷 101-118页

作者： Hongliang Liu Jingwen Song Huini Liu Jie Xu Lijuan Li School of Mathematics and Computational Science&Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan UniversityXiangtanHunan 411105China School of Automation and Electronic Information Xiangtan UniversityXiangtanHunan 411105China

In this paper,we propose a novel Legendre neural network combined with the extreme learning machine algorithm to solve variable coefficients linear delay differential-algebraic equations with weak ***,the solution interval is divided into multiple subintervals by weak discontinuity ***,Legendre neural network is used to eliminate the hidden layer by expanding the input pattern using Legendre polynomials on each ***,the parameters of the neural network are obtained by training with the extreme learning *** numerical examples show that the proposed method can effectively deal with the difficulty of numerical simulation caused by the discontinuities.

关键词： Convergence delay differential-algebraic equations Legendre activation function,neural network.

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Doubling Algorithm for Nonsymmetric Algebraic Riccati Equations Based on a Generalized Transformation

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Advances in Applied Mathematics and Mechanics 2018年第6期10卷 1327-1343页

作者： Bo Tang Yunqing Huang Ning Dong School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and EngineeringKey Laboratory of Intelligent Computing and Information Processing of Ministry of EducationXiangtan UniversityXiangtan 411105HunanChina School of Science Hunan City UniversityYiyang 413000HunanChina School of Science Hunan University of TechnologyZhuzhou 412000HunanChina

We consider computing the minimal nonnegative solution of the nonsymmetric algebraic Riccati equation with *** is well known that such equations can be efficiently solved via the structure-preserving doubling algorithm(SDA)with the shift-and-shrink transformation or the generalized Cayley *** this paper,we propose a more generalized transformation of which the shift-and-shrink transformation and the generalized Cayley transformation could be viewed as two special ***,the doubling algorithm based on the proposed generalized transformation is presented and shown to be ***,the convergence result and the comparison theorem on convergent rate are *** numerical experiments show that the doubling algorithm with the generalized transformation is efficient to derive the minimal nonnegative solution of nonsymmetric algebraic Riccati equation with M-matrix.

关键词： Shift-and-shrink transformation generalized Cayley transformation doubling algorithm nonsymmetric algebraic Riccati equation

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Exact and numerical stability analysis of reaction-diffusion equations with distributed delays

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Frontiers of Mathematics in China 2016年第1期11卷 189-205页

作者： Gengen ZHANG Aiguo XIAO School of Mathematics and Computational Science Hunan Key Laboratory for Computationand Simulation in Science and Engineering Xiangtan University Xiangtan 411105 China

This paper is concerned with the stability analysis of the exact and numerical solutions of the reaction-diffusion equations with distributed delays. This kind of partial integro-differential equations contains time memory term and delay parameter in the reaction term. Asymptotic stability and dissipativity of the equations with respect to perturbations of the initial condition are obtained. Moreover, the fully discrete approximation of the equations is given. We prove that the one-leg θ-method preserves stability and dissipativity of the underlying equations. Numerical example verifies the efficiency of the obtained method and the validity of the theoretical results.

关键词： keywords Reaction-diffusion equations distributed delay dissipativity,asymptotic stability

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Lower Bounds for Eigenvalues of the Stokes Operator

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Advances in Applied Mathematics and Mechanics 2013年第1期5卷 1-18页

作者： Jun Hu Yunqing Huang LMAM and School of Mathematical Sciences Peking UniversityBeijing 100871China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan UniversityXiangtan 411105China

In this paper,we propose a condition that can guarantee the lower bound property of the discrete eigenvalue produced by the finite element method for the Stokes *** check and prove this condition for four nonconformin... 详细信息

关键词： Lower bound eigenvalue Stokes operator

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Analysis of a two-grid method for semiconductor device problem

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Applied Mathematics and Mechanics(English Edition) 2021年第1期42卷 143-158页

作者： Ying LIU Yanping CHEN Yunqing HUANG Qingfeng LI School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and EngineeringXiangtan UniversityXiangtan 411105Hunan ProvinceChina College of Information and Intelligence Hunan Agricultural UniversityChangsha 410128China School of Mathematical Sciences South China Normal UniversityGuangzhou 510631China

The mathematical model of a semiconductor device is governed by a system of quasi-linear partial differential *** electric potential equation is approximated by a mixed finite element method,and the concentration equations are approximated by a standard Galerkin *** estimate the error of the numerical solutions in the sense of the *** linearize the full discrete scheme of the problem,we present an efficient two-grid method based on the idea of Newton *** main procedures are to solve the small scaled nonlinear equations on the coarse grid and then deal with the linear equations on the fine *** estimation for the two-grid solutions is analyzed in *** is shown that this method still achieves asymptotically optimal approximations as long as a mesh size satisfies H=O(h^1/2).Numerical experiments are given to illustrate the efficiency of the two-grid method.

关键词： two-grid method semiconductor device mixed finite element method Galerkin method L^q error estimate

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The correction operator for the canonical interpolation operator of the Adini element and the lower bounds of eigenvalues

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science China Mathematics 2012年第1期55卷 187-196页

作者： HU Jun HUANG YunQing LMAM and School of Mathematical Sciences Peking UniversityBeijing 100871Chinal Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan UniversityXiangtan 411105China

In this paper,we develop a correction operator for the canonical interpolation operator of the Adini *** use this new correction operator to analyze the discrete eigenvalues of the Adini element method for the fourth order elliptic eigenvalue problem in the three *** prove that the discrete eigenvalues are smaller than the exact ones.

关键词： the lower bound the Adini element the eigenvalue problem

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RECOVERY BASED FINITE ELEMENT METHOD FOR BIHARMONIC EQUATION IN 2D

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Journal of computational Mathematics 2020年第1期38卷 84-102页

作者： Yunqing Huang Huayi Wei Wei Yang Nianyu Yi Key Laboratory of Intelligent Computing&Information Processing of Ministry of Education School of Mathematics and Computational ScienceXiangtan UniversityXiangtan 411105China Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational ScienceXiangtan UniversityXiangtan 411105China

We design and numerically validate a recovery based linear finite element method for solving the biharmonic *** main idea is to replace the gradient operator▽on linear finite element space by G(▽)in the weak formulation of the biharmonic equation,where G is the recovery operator which recovers the piecewise constant function into the linear finite element *** operator G,Laplace operator△is replaced by▽·G(▽).Furthermore,the boundary condition on normal derivative▽u-n is treated by the boundary penalty *** explicit matrix expression of the proposed method is also *** examples on the uniform and adaptive meshes are presented to illustrate the correctness and effectiveness of the proposed method.

关键词： Biharmonic equation Linear finite element Recovery Adaptive

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A fast finite difference/finite element method for the two-dimensional distributed-order time-space fractional reaction-diffusion equation

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International Journal of Modeling, simulation, and Scientific Computing 2020年第2期11卷 115-132页

作者： Yaping Zhang Jiliang Cao Weiping Bu Aiguo Xiao School of Mathematics and Computational Science and Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University 411105 HunanP.R.China College of Science Shaoyang University 422000 ShaoyangP.R.China

In this work,we develop a finite difference/finite element method for the two-dimensional distributed-order time-space fractional reaction-diffusion equation(2D-DOTSFRDE)with low regularity solution at the initial time.A fast evaluation of the distributedorder time fractional derivative based on graded time mesh is obtained by substituting the weak singular kernel for the *** stability and convergence of the developed semi-discrete scheme to 2D-DOTSFRDE are *** the spatial approximation,the finite element method is *** convergence of the corresponding fully discrete scheme is ***,some numerical tests are given to verify the obtained theoretical results and to demonstrate the effectiveness of the method.

关键词： Distributed-order fractional derivative fractional reaction-diffusion equation fast evaluation graded mesh finite element method error estimate

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