2002年, 第20卷, 第2期　刊出日期：2002-03-15

  

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  ON THE CONVERGENCE OF PROJECTOR-SPLINES FOR THE NUMERICAL EVALUATION OF CERTAIN TWO-DIMENSIONAL CPV INTEGRALS

  Elisabetta Santi,M.G.Cimoroni

  Journal of Computational Mathematics. 2002, 20(2): 113-120.

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  In this paper, product formulas based on projector-splines for the numerical evaluation of 2-D CPV integrals are proposed. Convergence results are proved, numerical examples and comparisons are given.
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  ON THE CONVERGENCE OF IMPLICIT DIFFERENCE SCHEMES FOR HYPERBOLIC CONSERVATION LAWS

  Hua Zhong TANG(1),Hua Mo WU(2)

  Journal of Computational Mathematics. 2002, 20(2): 121-128.

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  This paper is to treat implicit difference approximations to hyperbolic conservation laws with non-convex flux. The convergence of the approximate solution toward the entropy solution is established for the general weighted implicit difference schemes,which include some well-known implicit and explicit difference schemes.
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  MULTIGRID METHODS FOR THE GENERALIZED STOKES EQUATIONS BASED ON MIXED FINITE ELEMENT METHODS

  Qing Ping DENG,Xiao Ping FENG

  Journal of Computational Mathematics. 2002, 20(2): 129-152.

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  Multigrid methods are developed and analyzed for the generalized stationary Stokes equations which are discretized by various mixed finite element methods. In this paper, the multigrid algorithm, the criterion for prolongation operators and the convergence analysis are all established in an abstract and element-independent fashion.It is proven that the multigrid algorithm converges optimally if the prolongation operator satisfies the criterion. To utilize the abstract result, more than ten well-known mixed finite elements for the Stokes problems are discussed in detail and examples of prolongation operators are constructed explicitly. For nonconforming elements, it is shown that the usual local averaging technique for constructing prolongation operators can be replaced by a computationally cheaper alternative, random choice technique. Moreover, since the algorithm and analysis allows using of nonnested meshes, the abstract result also applies to low order mixed finite elements, which are usually stable only for some special mesh structures.
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  LEAST-SQUARES MIXED FINITE ELEMENT METHODS FOR NONLINEAR PARABOLIC PROBLEMS

  Dan Ping YANG

  Journal of Computational Mathematics. 2002, 20(2): 159-164.

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  Two least-squares mixed finite element schemes are formulated to solve the initial-boundary value problem of a nonlinear parabolic partial differential equation and the convergence of these schemes are analyzed.
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  A PRECONDITIONER FOR COUPLING SYSTEM OF NATURAL BOUNDARY ELEMENT AND COMPOSITE GRID FINITE ELEMENT

  Qi Ya HU(1),De Hao YU(2)

  Journal of Computational Mathematics. 2002, 20(2): 165-174.

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  In this paper, based on the natural boundary reduction advanced by Feng and Yu, we discuss a coupling BEM with FEM for the Dirichlet exterior problems. In this method the finite element grids consist of fine grid and coarse grid so that the singularity at the couner points van be bandled conveniently. In order to solve the coupling system by the preconditioning conjugate gradient method, we construct a simple preconditioner for the "stiffness" matrix. Some error estimates of the corresponding approximate solution and condition number estimate of the preconditioned matrix are also obtained.
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  EFFICIENT SIXTH ORDER P-STABLE METHODS WITH MINIMAL LOCAL TRUNCATION ERROR FOR y

  Kai Li XIANG(1),R.M.Thmoas(2)

  Journal of Computational Mathematics. 2002, 20(2): 175-184.

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  A family of symmetric (hybrid) two step sixth P-stable methods for the accurate numerical integration of second order periodic initial value problems have been considered in this paper. These methods, which require only three (new) function evaluation per iteration and per step integration. These methods have minimal local truncation error (LTE) and smaller phase-lag of sixth order than some sixth orders P-stable methods in [1-3,10-11]. The theoretical and numerical results show that these methods in this paper are more accurate and eficient than efficient than some methods proposed in [1-3,10].
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  EXPANSION OF STEP-TRANSITION OPERATOR OF MULTI-STEP METHOD AND ITS APPLICATIONS (Ⅰ)

  Yi Fa TANG

  Journal of Computational Mathematics. 2002, 20(2): 185-196.

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  We expand the step-transition operator of any linear multi-step method with order s≥ 2 up to O(Ts+5). And through examples we show how much the perturbation of the step-transition operator caused by the error of initial value is.
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  DOMAIN DECOMPOSITION METHODS WITH NONMATCHING GRIDS FOR THE UNILATERAL PROBLEM

  Ping LUO(1),Guo Ping LIANG(2)

  Journal of Computational Mathematics. 2002, 20(2): 197-206.

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  This paper is devoted to the construction of domain decomposition methods with non-matching grids based on mixed finite element methods for the unilateral problem. The existence and uniqueness of solution are discussed and optimal error bounds are obtained. Furhtermore, global superconvergence estimates are given.
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  BIVARIATE LAGRANGE-TYPE VECTOR VALUED RATIONAL INTERPOLANTS

  Chuan Qing GU(1),Gong Qing ZHU(2)

  Journal of Computational Mathematics. 2002, 20(2): 207-216.

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  An axiomatic definition to bivariate vector valued rational interpolation on distinct plane interpolation points is at first presented in this paper. A two-variable vector valued rational interpolation formula is explicitly constructed in the following form:the determinantal formulas for denominatorscalar polynomials and for numerator vector polynomials, which possess Lagrange-type basic function expressions. A practical criterion of existence and uniqueness for interpolation is obtained. In contrast to the underlying methok, the method of bivariate Thiele-type vector valued rational interpolation is reviewed.
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  ASYMPTOTIC STABILITY FOR GAUSS METHODS FOR NEUTRAL DELAY DIFFERENTIAL EQUATIONS

  Birama Sory SIDIBE,Ming Zhu LIU

  Journal of Computational Mathematics. 2002, 20(2): 217-224.

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  In [4] we proved that all Gauss methods areNT(O)-compatible for neutral delay differential equations (NDDEs) of the form:$$\begin{array}{l} y'(t)=ay(t)+by(t-\tau)+cy'(t-\tau), \ \ t>0, \ y(t)=g(t),\ \ -\tau\leq t\leq 0, \end{array}\tag{0.1}$$ where a, b, c are real, $\tau > 0$, g(t) is a continuous real valued function. In this paper we are going to use the theory of order stars to characterize the asymptotic stability properties of Gauss methods for NDDEs. And then proved that all Gauss methods are $N\tau(0)-$stable.