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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 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 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 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.

THe LARGe TIMe CONVeRGeNCe OF SPeCTRAL MeTHOD FOR GeNeRALIZeD KURAMOTO-SIVASHINSKY eQUATION (Ⅱ)

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Journal of computational Mathematics 1998年第3期16卷 203-212页

作者： Xin-ming Xiang (shanghai normal university, shanghai 200234, china) 上海师范大学上海

In this paper, we study fully discrete spectral method and long time behavior of solution of generalized Kuramoto-Sivashinsky equation with periodic initial condition. We prove that the large time error estimation for fully discrete solution of spectral method. We prove the existence of approximate attractors AN, ANk respectively and d(AN, A) → 0, d(ANk, A) → 0.

关键词： Kuramoto- Sivashinsky equation,large time convergence Approximate attractor Upper semicontinuity of attractors.

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 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.

CURVILINeAR PATHS AND TRUST ReGION MeTHODS WITH NONMONOTONIC BACK TRACKING TeCHNIQUe FOR UNCONSTRAINeD OPTIMIZATION

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Journal of computational Mathematics 2001年第3期19卷 241-258页

作者： De-tong Zhu (Department of Mathematics, shanghai normal university, shanghai 200234, china) 上海师范大学上海 200234

Focuses on a study which examined the modification of type approximate trust region methods via two curvilinear paths for unconstrained optimization. Properties of the curvilinear paths; Description of a method which combines line search technique with an approximate trust region algorithm; Information on the convergence analysis; Details on the numerical experiments.

关键词： curvilinear paths trust region methods nonmonotonic technique unconstrained optimization

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 241000, china 2 division of computational science, e-institutes of shanghai universities, at SJTU, shanghai 200240, china Anhui normal university Wuhu 241000 China division of computational science 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

JACOBI SPeCTRAL APPROXIMATIONS TO DIFFeReNTIALeQUATIONS ON THe HALF LINe

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Journal of computational Mathematics 2000年第1期18卷 95-112页

作者： Ben-yu Guo(Department of Mathematics, shanghai normal university, shanghai 200234, china)(COM2MAC, Pohang university of science and Technology, Pohang, Korea) 上海师范大学上海 200234

Presents a study which investigated some Jacobi approximations which are used for numerical solutions of differential equations on the half line. Application of the approximations to problems on unbounded domains; Alg... 详细信息

关键词： Jacobi spectral approximations differential equations on the half line stability and convergence

THe MINIMAL CLOSeD NON-TRIVIAL IDeALS OF TOePLITZ ALGeBRAS ON DISCReTe GROUPS

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Chinese Annals of Mathematics,Series B 2000年第3期21卷 367-374页

作者： XU QINGXIANG(Department of Mathematics, shanghai normal university, shanghai 200234, china.) e-mail:qxxu@*** Department of Mathematics Shanghai Normal University Shanghai 200234 China

Let G be a discrete group and (G, G+) an ordered group. Let (G, GF) be the minimal quasiordered group containing (G, G+). Let G+ (G) and (G) be the corresponding Toeplitz algebras, and γGF,G+ the natural C*-algebra morphism from G+ (G) to GF(G). This paper studies the connection between Ker GF,G+ and the minimal closed ideal ofTG+ (G). It is proved that if G is amenable and GF≠G+, then Ker γGF,G+ is exactly the minimal closed non-trivial ideal of G+ (G). As an application, in the last part of this paper, a character of K-groups of Toeplitz algebras on ordered groups is clarified.

关键词： Discrete group Toeplitz algebra Minimal ideal

JACOBI SPeCTRAL MeTHODS FOR MULTIPLe- DIMeNSIONAL SINGULAR DIFFeReNTIAL eQUATIONS

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Journal of computational Mathematics 2003年第3期21卷 325-338页

作者： Li-Han Wang Ben-yu Guo (Department of Mathematics, shanghai normal university, shanghai 200234, china) Department of Mathematics Shanghai Normal University 上海 200234

Jacobi polynomial approximations in multiple dimensions are investigated. They are applied to numerical solutions of singular differential equations. The convergence analysis and numerical results show their advantages.

关键词： Jacobi approximations Multiple dimensions.