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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..2..,China division of computational science,e-Institute of shanghai universities,shanghai Normal Benyu Guo Department of Mathematics,shanghai Normal University,shanghai 2..2..,China division of computational science,e-Institute of shanghai universities,shanghai,China Department of Mathematics East China Normal University Shanghai 200241 China division of computational science E-Institute of Shanghai Universities Shanghai Normal University Shanghai 200234 China Department of Mathematics Shanghai Normal University Shanghai 200234 China division of computational science 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.

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..2..,China Scientific Computing Key Laboratory of shanghai universities division of computational science 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.

A CLASS OF NONLINeAR SINGULARLY PeRTURBeD INITIAL BOUNDARY VALUe PROBLeMS FOR ReACTION DIFFUSION eQUATIONS WITH BOUNDARY PeRTURBATION

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Applied Mathematics(A Journal of Chinese universities) 2007年第2期22卷 201-206页

作者： Mo Jiaqi Department of Mathematics, Anhui Normal University, Wuhu 2..000, China Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China division of computational science, e-institutes of shanghai universities at sjtu,{2..China. Department of Mathematics Anhui Normal University Wuhu 241000 China

A class of nonlinear initial boundary value problems for reaction diffusion equations with boundary perturbation is considered. Under suitable conditions and using the theory of differential inequalities the asymptoti... 详细信息

关键词： nonlinear reaction diffusion singular perturbation boundary perturbation

Variational iteration solving method of a sea-air oscillator model for the eNSO

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Progress in Natural science:Materials International 2007年第2期17卷 230-232页

作者： MO Jiaqi, LIN Wantao and WANG Hui ( Department of Mathematics, Anhui Normal University, Wuhu 241000, China division of computational science, e-institutes of {2..universities, at sjtu, shanghai 2.02.0, China LASG, Institute of Atmospheric Physics, Chinese Academy of sciences, Beijing 100029, China Chinese Academy of Meteorological sciences, Beijing 100081, China) [a]Department of Mathematics Anhui Normal University Wuhu China [b]division of computational science E-Institures of Shanghai Universities at SJTU Shanghai China [c]LASG Institute of Atmospheric Physics Chinese Academy of Sciences Bejing China [d]Chinese Academy of Meterological sciences Beijing China

A time delay equation for sea-air oscillator model is studied. The aim is to create an asymtotic solving method of nonlinear equation for the eNSO model. And based on a class of oscillators of eNSO model, employing the variational iteration method, the approximate solution of corresponding problem is obtained. It is proven from the results that the method of variational iteration method can be used for analyzing the sea surface temperature anomaly in the equatorial eastern Pacific of the atmosphere-ocean oscillation for eNSO model.

关键词： Nonlinear problem, time delay, el Nino-Southern oscillator model variational iteration.

Finite element analysis for general elastic multi-structures

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science China Mathematics 2006年第1期49卷 109-129页

作者： HUANG Jianguo, SHI Zhongci & XU Yifeng Department of Mathematics, shanghai Jiao long University, shanghai 2.02.0, China {2..e-lnstitute of shanghai universities, shanghai Normal University, shanghai 2..2.., China Institute of computational Mathematics, Academy of Mathematics and Systems science, Chinese Academy of sciences, Beijing 100080, China Department of Mathematics, Chinese University of Hong Kong, Shatin, N. T., Hong Kong, China Department of Mathematics Shanghai Jiao Tong University Shanghai 200240 China division of computational science E-Institute of Shanghai Universities Shanghai Normal University Shanghai 200234 China Institute of computational Mathematics Academy of Mathematics Systems science Chinese Academy of sciences Beijing 100080 China Department of Mathematics Chinese University of Hong Kong Shatin N. T. Hong Kong China

A finite element method is introduced to solve the general elastic multi-structure problem, in which the displacements on bodies, the longitudinal displacements on plates and the longitudinal displacements on beams are discretized using conforming linear elements, the rotational angles on beams are discretized using conforming elements of second order, the transverse displacements on plates and beams are discretized by the Morley elements and the Hermite elements of third order, respectively. The generalized Korn's inequality is established on related nonconforming element spaces, which implies the unique solvability of the finite element method. Finally, the optimal error estimate in the energy norm is derived for the method.

关键词： elastic multi-structures, finite elements, generalized Korn's inequality, unique solvability, error estimates.

Biomarkers of neurodegenerative disorders: How good are they?

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Cell Research 2004年第5期14卷 347-358页

作者： Varun RACHAKONDA Department of Neurology Baylor College of Medicine Houston TX USA

Biomarkers are very important indicators of normal and abnormal biological processes. Specific changes in pathologies, biochemistries and genetics can give us comprehensive information regarding the nature of any particular disease. A good biomarker should be precise and reliable, distinguishable between normal and interested disease, and differential between different diseases. It is believed that biomarkers have great potential in predicting chances for diseases, aiding in early diagnosis, and setting standards for the development of new remedies to treat diseases. New technologies have enabled scientists to identify biomarkers of several different neurodegenerative diseases. The followings, for instance, are only a few of the many new biomarkers that have been recently identified: the phosphorylated tau protein and aggregated β-amyloid peptide for Alzheimer’s disease (AD), α-synuclein contained Lewy bodies and altered dopamine transporter (DAT) imaging for Parkinson’s disease (PD), SOD mutations for familial amyotrophic lateral sclerosis (ALS), and CAG repeats resulted from Huntington’s gene mutations in Huntington’s disease (HD). This article will focus on the most-recent findings of biomarkers belonging to the four mentioned neurodegenerative diseases.

关键词： Alzheimer’s disease Parkinson’s disease Amyotrophic Lateral Sclerosis Huntington’s disease biomarkers.

A lumped mass finite element method for vibration analysis of elastic plate-plate structures

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science China Mathematics 2010年第6期53卷 1453-1474页

作者： LAI JunJiang1,HUANG JianGuo2..,& SHI ZhongCi4 1Department of Mathematics,Minjiang University,Fuzhou 350108,China 2..partment of Mathematics,shanghai Jiao Tong University,shanghai {2..hina 3division of computational science,e-Institute of shanghai universities,shanghai Normal University,shanghai 2..2..,China 4Institute of computational Mathematics,Academy of Mathematics and Systems science,Chinese Academy of sciences,Beijing 100190,China 1. Department of Mathematics Minjiang University Fuzhou 350108 China2. Department of Mathematics Shanghai Jiao Tong University Shanghai 200240 China3. Division of Computational Science E-Institute of Shanghai Universities Shanghai Normal University Shanghai 200234 China4. Institute of Computational Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

The fully discrete lumped mass finite element method is proposed for vibration analysis of elastic plate-plate *** the space directions,the longitudinal displacements on plates are discretized by conforming linear elements,and the transverse displacements are discretized by the Morley *** means of the second order central difference for discretizing the time derivative and the technique of lumped masses,a fully discrete lumped mass finite element method is obtained,and two approaches to choosing the initial functions are also *** error analysis for the method in the energy norm is established,and some numerical examples are included to validate the theoretical analysis.

关键词： vibration analysis plate-plate structures lumped mass FeM error analysis

NONLINeAR ReACTION DIFFUSION PROBLeMS WITH ULTRA PARABOLIC LIMITING eQUATIONS

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Applied Mathematics(A Journal of Chinese universities) 2007年第3期22卷 286-290页

作者： Mo Jiaqi Dept.of Math.,Anhui Normal Univ.,Wuhu 241000,China Dept.of Math.,Huzhou Teachers College,Huzhou 313000,China division of computational science,e-institutes of {2..Univ.at sjtu,{2..2.02.0,China. Dept. of Math. Anhui Normal Univ. Wuhu 241000 China Dept. of Math. Huzhou Teachers College Huzhou 313000 China division of computational science E-Institutes of Shanghai Univ. at SJTU Shanghai 200240 China

In this paper the nonlinear reaction diffusion problems with ultraparabolic equations are considered. By using comparison theorem, the existence, uniqueness and asymptotic behavior of solution for the problem are stud... 详细信息

关键词： nonlinear ultra-parabolic equation reaction diffusion asymptotic behavior comparison theorem.

SINGULARLY PeRTURBeD SOLUTION TO SeMILINeAR HIGHeR ORDeR ReACTION DIFFUSION eQUATIONS WITH TWO PARAMeTeRS

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Annals of Differential equations 2009年第1期25卷 91-96页

作者： Yao Jingsun, Mo Jiaqi (Dept. of Math., Anhui Normal University, Wuhu 241000, Anhui division of computational science, e-institutes of {2..universities, at sjtu, shanghai 2.02.0) division of computational science E-Institutes of Shanghai Universitiesat SJTU Shanghai 200240

A boundary value problem for semilinear higher order reaction diffusion equa-tions with two parameters is considered. Under suitable conditions, by the theory of differential inequalities, the existence and asymptotic... 详细信息

关键词： semilinear two parameters asymptotic solution singular perturba-tion