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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 241000, china Department of Mathematics, Huzhou Teachers College, Huzhou 313000, china division of computational science, e-institutes of shanghai universities at sjtu, shanghai 200240, china. Department of Mathematics Anhui Normal University Wuhu China Department of Mathematics Huzhou Teachers College Huzhou China division of computational science E-Institutes of Shanghai Universities at SJTU Shanghai 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 shanghai universities, at sjtu, shanghai 200240, china LASG, Institute of Atmospheric Physics, Chinese Academy of sciences, Beijing 100029, china Chinese Academy of Meteorological sciences, Beijing 100081, china) Department of Mathematics Anhui Normal University Wuhu 241000 China division of computational science E-Institutes of Shanghai Universities at SJTU Shanghai 200240 China LASG Institute of Atmospheric Physics Chinese Academy of Sciences Beijing 100029 China Chinese Academy of Meteorological sciences Beijing 100081 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.

THe SOLVABILITY FOR A CLASS OF SINGULARLY PeRTURBeD QUASI-LINeAR DIFFeReNTIAL SYSTeM

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Acta Mathematica Scientia 2008年第3期28卷 495-500页

作者：莫嘉琪王辉林万涛 Department of Mathemtics Anhui Normal University division of computational science E-Institutes of Shanghai Universities at SJTUShanghai 200240China Department of Mathematics Huzhou Teachers'CollegeHuzhou 313000China Chinese Academy of Meteorological sciences LASG Institute of Atmospheric PhysicsChinese Academy of Sciences

The solvability for a class of singularly perturbed Robin problem of quasilinear differential system is considered. Using the boundary layer corrective method the formal asymptotic solution is constructed. And using t... 详细信息

关键词： Solvability singular perturbation differential system boundary layer

Perturbed solution of sea-air oscillator for the el Nino/ La Nina-Southern Oscillation mechanism

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Acta Oceanologica Sinica 2009年第3期28卷 1-4页

作者： ZHOU Xianchun LIN Yihua WANG Hui MO Jiaqi College of electronic and Information engineering Nanjing University of information Science and Technology Nanjing 210044 China division of computational science E-Institutes of Shanghai Universities at SJTU Shanghai 200240 China State Key Laboratory of Numerical Modeling for Atmospheric sciences and Geophysical Fluid Dynamics Institute of Atmospheric Physics Chinese Academy of Sciences Beijing 100029 China National Marine environmental Forecastins Center Beijing 100081 China Department of Mathematics Anhui Normal University Wuhu 241000 China

A class of coupled system of the e1 Nino/La Nina-Southern Oscillation （eNSO） mechanism is studied. Using the perturbed theory, the asymptotic expansions of the solution for eNSO model are obtained and the asymptotic... 详细信息

关键词： nonlinear perturbation theory e1 Nino/La Nina-Southern Oscillation model

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 200241,china division of computational science,e-Institute of shanghai universities,shanghai Normal Benyu Guo Department of Mathematics,shanghai Normal University,shanghai 200234,china division of computational science,e-Institute of shanghai universities,shanghai,china Department of Mathematics East China Normal University ShangHai Department of Mathematics Shanghai Normal University ShangHai

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 200234,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.

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 200240, china division of computational science, e-lnstitute of shanghai universities, shanghai Normal University, shanghai 200234, 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 China division of computational science E-Institute of Shanghai Universities Shanghai Normal University Shanghai China Institute of computational Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China Department of Mathematics Chinese University of Hong Kong 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.

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 shanghai Univ.at sjtu,shanghai 200240,china. Dept. of Math. Anhui Normal Univ. Wuhu China Dept. of Math. Huzhou Teachers College Huzhou China division of computational science E-Institutes of Shanghai Univ. at SJTU Shanghai 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.

An extended stochastic response surface method for random field problems

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Acta Mechanica Sinica 2007年第4期23卷 445-450页

作者： Shuping Huang Xinjian Kou shanghai Jiaotong University,shanghai 200240,china shanghai Jiaotong University Shanghai China

An efficient and accurate uncertainty propagation methodology for mechanics problems with random fields is developed in this paper. This methodology is based on the stochastic response surface method （SRSM） which has been previously proposed for problems dealing with random variables only. This paper extends SRSM to problems involving random fields or random processes fields. The favorable property of SRSM lies in that the deterministic computational model can be treated as a black box, as in the case of commercial finite element codes. Numerical examples are used to highlight the features of this technique and to demonstrate the accuracy and efficiency of the proposed method. A comparison with Monte Carlo simulation shows that the proposed method can achieve numerical results close to those from Monte Carlo simulation while dramatically reducing the number of deterministic finite element runs.

关键词： Stochastic response surface Karhunen-Loeve expansion Polynomial chaos Random field Stochastic finite elements