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ASYMPTOTIC SOLUTION TO MODEL FOR A CLASS OF VIRUS TRANSMISSION

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Annals of Differential Equations 2010年第4期26卷 436-441页

作者： Jiaqi Mo 1,2., Jingsun Yao 1 (1. Dept. of Math., Anhui Normal University, Wuhu 2.1003, Anhui 2. division of computational science, E-Institutes of Shanghai Universities, at SJTU, Shanghai 2.02.0)

In this paper, a class of HIV virus transmission is considered. The transmissive dynamic model for the HIV virus is described. Using the functional-variational iteration theory, the rule for human group in the epidemi... 详细信息

关键词： HIV virus nonlinear functional-variational iteration

EXISTENCE OF SOLUTIONS TO COUPLED FRACTIONAL ORDER SYSTEMS WITH THREE-POINT BOUNDARY CONDITIONS

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Annals of Differential Equations 2011年第2期27卷 228-233页

作者： Xianyin Wu 1 , Feng Xie 1,2., Huacheng Zhou 1 (1. Dept. of Applied Math., Donghua University, Shanghai 2.162. 2. division of computational science, E-Institute of Shanghai Universities, at SJTU, Shanghai 2.0030)

This paper investigates a class of coupled systems of nonlinear fractional differential equations with three-point boundary conditions. Under suitable conditions the existence of solutions is obtained using the Schaud... 详细信息

关键词： fractional differential equations boundary value problem Schauder fixed point theorem

THE GENERALIZED FUNCTIONAL-VARIATION SOLVING METHODS FOR NONLINEAR REACTION DIFFUSION IN BIONOMICS OF SPECIES GROUPS

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Annals of Differential Equations 2008年第2期24卷 193-196页

作者： Mo Jiaqi1,2.Yao Jingsun1(1. Dept. of Math.,Anhui Normal University,Wuhu 2.1000,Anhui 2. division of computational science,E-Institutes of Shanghai Universities at SJTU,Shanghai 2.02.0)

In this paper,a class of nonlinear predator-prey for reaction diffusion system is considered. Using the generalized functional-variational theory,the approximate expressions of the solution for nonlinear bionomics of ... 详细信息

关键词： nonlinear predator-prey reaction diffusion variational

VARIATIONAL ITERATION SOLVING METHOD FOR SEA-AIR OSCILLATOR MODEL OF INTERDECADAL CLIMATE FLUCTUATIONS

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Chinese Geographical science 2005年第3期 37-40页

作者： MO Jia-qi1, 2. LIN Yi-hua3, WANG Hui4 (1. Department of Mathematics,Anhui Normal University,Wuhu 2.1000,P. R. China 2. division of computational science E-Institutes of Shanghai Universities at Shanghai Jiaotong University,Shanghai 2.02.0,P. R. China 3. Institute of Atmospheric Physics,Chinese Academy of sciences,Beijing 10002.,P. R. China 4. Chinese Academy of Meteorological sciences,Beijing 100081,P. R.China) Department of Mathematics A nhui Normal UniversityWuhu 241000P. R. China division of computational {2. E-Institutes of Shanghai Universities at Shanghai Jiaotong UniversityShanghai 200240P. R. China Institute of Atmospheric Physics Chinese Academy of SciencesBeijing 100029P. R. China Chinese Academy of Meteorological sciences Beijing 100081P. R. China

Atmospheric physics is a very complicated natural phenomenon and needs to simplify its basic models for the sea-air oscillator. And it is solved by using the approximate method. The variational iteration method is a simple and valid method. In this paper the coupled system for a sea-air oscillator model of interdecadal climate fluctuations is considered. Firstly, through introducing a set of functions, and computing the variations, the Lagrange multipliers are obtained. And then, the generalized expressions of variational iteration are constructed. Finally, through selecting appropriate initial iteration from the iteration expressions, the approximations of solution for the sea-air oscillator model are solved successively.

关键词： nonlinear variational iteration El Nio-Southern Oscillator model

Homotopic mapping solving method for gain fluency of a laser pulse amplifier

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science China(Physics,Mechanics & Astronomy) 2009年第7期52卷 1007-1010页

作者： MO JiaQi1,2.1 Anhui Normal University, Wuhu 2.1000, China 2.division of computational {2., E-Institutes of Shanghai Universities, at SJTU, Shanghai 2.02.0, China Anhui Normal University Wuhu 241000 China division of computational {2. E-Institutes of Shanghai Universities at SJTU Shanghai 200240 China

The model for gain fluency of a laser pulse amplifier is studied. Using the homotopic mapping method, firstly, the system of the original model is packed up standardization; secondly, introducing a homotopic mapping, taking the property of the mapping, inducing a contrived parameter, the solving of a nonlinear problem translates into the solving of a linear problem. Then the approximate expressions of the solution for the corresponding model are obtained. And the precision for the approximate solution is compared. It illuminates that the obtained approximate solution using the homotopic mapping method possesses higher approximate degree. At one time, the expansion of solution through the homotopic mapping method can be kept in the analytic operation. Thus it also enables us through differential and integral operations to obtain other physics behavior for the gain fluency of laser pulse amplifier.

关键词： nonlinear homotopic mapping laser pulse amplifier

A MONOTONE COMPACT IMPLICIT SCHEME FOR NONLINEAR REACTION-DIFFUSION EQUATIONS

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Journal of computational Mathematics 2008年第2期26卷 123-148页

作者： Yuanming Wang Department of Mathematics,East China Normal University,Shanghai 2.02.1,China division of computational {2.,E-Institute of Shanghai Universities,Shanghai Normal Benyu Guo Department of Mathematics,Shanghai Normal University,Shanghai 2.02.4,China division of computational {2.,E-Institute of Shanghai Universities,Shanghai,China Department of Mathematics East China Normal University Shanghai 200241 China division of computational {2. E-Institute of Shanghai Universities Shanghai Normal University Shanghai 200234 China Department of Mathematics Shanghai Normal University Shanghai 200234 China division of computational {2. E-Institute of Shanghai Universities Shanghai China

A monotone compact implicit finite difference scheme with fourth-order accuracy in space and second-order in time is proposed for solving nonlinear reaction-diffusion equations. An accelerated monotone iterative method for the resulting discrete problem is presented. The sequence of iteration converges monotonically to the unique solution of the discrete problem, and the convergence rate is either quadratic or nearly quadratic, depending on the property of the nonlinear reaction. The numerical results illustrate the high accuracy of the proposed scheme and the rapid convergence rate *** iteration.

关键词： Nonlinear reaction-diffusion equation Monotone compact implicit scheme High accuracy Monotone iteration Rapid convergence rate.

Two-dimensional simulation of Poiseuille-Rayleigh-Bénard flows in binary fluids with Soret effect

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Progress in Natural science:Materials International 2007年第12期17卷 1389-1396页

作者： Hu Jun1 and Yin Xieyuan2.1. Institute of Applied Physics and computational Mathematics, Beijing 100088, China 2. Department of Modern Mechanics, University of science and Technology of China, Hefei 2.002., China) Institute of Applied Physics and computational Mathematics Beijing 100088 China Department of Modern Mechanics University of Science and Technology of China Hefei 230027 China

Poiseuille-Rayleigh-Bénard flows in binary fluids with Soret effect are directly simulated by a mixed finite element method. A temperature perturbation is used as an initial disturbed source for the basic parallel flows. The whole spatio-temporal evolution of the binary fluid flows is exhibited: initially only the disturbed mode with the wavenumber k=π is amplified while others are damped, and continuously the amplified mode grows further and the nonlinear effect becomes important; after a nonlinear evolution transition the flow system evolves finally into a periodic right traveling wave.

关键词： Poiseuille-Rayleigh-Bénard flow Soret effect through-flow.

Mathematical stencil and its application in finite difference approximation to the Poisson equation

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science China Mathematics 2005年第10期48卷 1421-1429页

作者： FENG Hui~1 ZHANG Baolin~(1,2. & LIU Yang~1 1. Department of Mathematics,Wuhan University,Wuhan 430072.China 2. Laboratory of computational Physics,Institute of Applied Physics and computational Mathematics,Beijing 100088. China 1. Department of Mathematics Wuhan University 430072 Wuhan China 2. Laboratory of computational Physics Institute of Applied Physics and Computational Mathematics 100088 Beijing China

The concept of mathematical stencil and the strategy of stencil elimination for solving the finite difference equation is presented, and then a new type of the iteration algorithm is established for the Poisson equation. The new algorithm has not only the obvious property of parallelism, but also faster convergence rate than that of the classical Jacobi iteration. Numerical experiments show that the time for the new algorithm is less than that of Jacobi and Gauss-Seidel methods to obtain the same precision, and the computational velocity increases obviously when the new iterative method, instead of Jacobi method, is applied to polish operation in multi-grid method, furthermore, the polynomial acceleration method is still applicable to the new iterative method.

关键词： mathematical stencil, stencil elimination, Poisson equation, finite difference, iterative algorithm,parallelism.

ON NON-ISOTROPIC JACOBI PSEUDOSPECTRAL METHOD

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Journal of computational Mathematics 2008年第4期26卷 511-535页

作者： Benyu Guo Keji Zhang Department of Mathematics,Shanghai Normal University,Shanghai 2.02.4,China Scientific Computing Key Laboratory of Shanghai Universities division of computational {2. of E-Institute of Shanghai Universities Department of Mathematics Shanghai Normal University Shanghai 200234

In this paper, a non-isotropic Jacobi pseudospectral method is proposed and its appli- cations are considered. Some results on the multi-dimensional Jacobi-Gauss type interpolation and the related Bernstein-Jackson type inequalities are established, which play an important role in pseudospectral method. The pseudospectral method is applied to a twodimensional singular problem and a problem on axisymmetric domain. The convergence of proposed schemes is established. Numerical results demonstrate the efficiency of the proposed method.

关键词： Jacobi pseudospectral method in multiple dimensions Jacobi-Gauss type inter-polation Bernstein-Jackson type inequalities Singular problem Problem on axisymmetricdomain.