In this paper we consider mainly low order symplectic (or linear symplectic)partitioned Runge-Kutta methods of one kind of Hamiltonian systems for wave equations. Stability conditions for all two-stage explicitly partitioned Runge-Kutta methods with order 2 are disscussed. In addition some methods with low-order are applied to more general wave equations.

1．介绍非线性互补问题，记作NCP（F0）；是指求XRn使得其中的：RNCP有各种不同形式的推广．例如，一种广泛的互补问题，记作NCP（F1，F2，…，FN），是指求xRn使得其中马：＊”＋＊”，马杜）是马（x）的第7个分量·NCP（凡）的发展及其应用在数学规划领域己经有很长的历...

In this paper, a new matrix pade approximants which is based on generalized inverse is obtained. It is different from original matrix pade approximants in that it need not use multiplication of matrixces in its constructive process, hence, lefthanded pade approximants is same as right-handed ones in the cases. Generalized inverse matrix pade approximants can be computed by two methods: (i) the determinantal formula for denoninator polynomials; (ii) matrix -algorithm. The results in the paper are verified by some numerical examples.

The paper presents a new method to identify the acoustic speed and density simultaneously. Its distinguishing feature is directly on the baize of differential equations without introducing integral equations in the whole precedure. The algorithm is simple and fast, which easily come true on computers.

A generalized nonlinear least squares problem is converted into two subproblems, and two new algorithms for these two subproblems are proposed. The superlinear convergence of the algorithms is proved even if the subproblem 1 is solved by the steepest descent method which is only linearly convergent, and some numerical examples are given, which also show the efficience of the algorithms.

This paper presents a class of r-point r+1 order A-stable implicit one-block methods with nonderogatory coefficent matrix having only two different positive eigenvalues (abbreviated term TIBM), and a Newton-like iterative method for solving nonlinear equation system produced from the TIBM. The paper proposes also a implementation strategy (TIBMS) with variable stepsize and variable method by means of combination TIBM with EIBM (Economical Implicit Single-Block Methods). Theoretical analysis and numerical test indicate that this strategy will be hopeful for solving initial-value problems of Stiff ODEs on parallel computer.

A second order accurate implicit finite difference scheme CNMT2 is proposed in this paper for the unsteady incompressible Navier-Stokes equations. It is proved that the scheme is unconditionally nonlinearly stable on smoothly nonuniform halfstaggered meshes; this stability also holds for this scheme with the pressure correction projection method. However, it is found that the pressure correction projection method may lead to deviation problems in practical simulation of high Re flow;the reason and the cure is given in this paper in terms of differential-algebraic equations.

Let D be a bounded,simply connected domain in the plane and let F(θ, k, αn.)be the far field pattern arising from acoustic plane wave un(x) = exp(ikx·αn),where αn is a unit vecter and k is the wave number. It is assumed that the total filed satisfied homogeneous Dirichlet boundary condition on D. In this paper, a method is presented for recovering D given the far field patterns F(θ, k, αn) for all θ in some interval [a, a + ] strictly contained in [0, 2π] and a numerical method and some examples are presented.

(1) A staggered mesh compact difference scheme is presented for solving the unsteady viscous incompressible Navier-Stokes equations. It is fourth order accurate both in the spatial direction and in the time direction, at least third order accurate on the boundary; (2) Describe a pressure-Poisson-equation that is equivalent to the discrete continuity equation provided the discrete momentum equations remain. The discrete continuity equation may have derivative boundary conditions,e.g., the compact difference scheme; (3) A new ADI iterative method is proposed.The pressure-Poisson-equation is in the discrete form. It is difficult to be solved with a usual ADI method. We translate it to be tridiagonal in each spatial direction of each step of the ADI iterations, then add a pseudo time term to get a tridiagonal equation which is easily to be solved; (4) The driven flow in a square cavity with Re = 10000 is simulated numerically.

In the present paper, the authors suggest an algorithm to evaluate the multivariate normal integrals under the supposition that the correlation matrix R is quasi-decomposable, in which we have rij = aiaj for most i, j, and rij = aiaj + bij for the others, where bij's are the nonzero deviations. The algorithm makes the high-dimensional normal distribution reduce to a 2-dimensional or 3-dimensional integral which can be evaluated by the numerical method with a high precision.Our supposition is close to what we encounter in practice. When correlation matrix is arbitrary, we suggest an approximate algorithm with a medium precision, it is, in general, better than some approximate algorithms. The simulation results of about 20000 high-dimensional integrals showed that the present algorithms were very efficient.

Under the assumption that the function is analytic, Smale presents a wellknown criterion α which is used to study the behaviours of the convergence of Newton's method for finding zeros of a function and establishes a complete theory.In this paper we reestablish the whole theory of Smale's in the assumption that the function is the second continuously differeatiable.

In this paper, the Large-time problem of generalized Burgers equations in twodimensions is considered, semidiscrete and completely discrete spectral approximations are constracted, and error estimates of optimal order that hold uniformly onthe unbounded time interval 0 ≤t＜ are obtained.

As a standard result in perturbation theory, Weyl theorem has been establishedanalogously for singular value problem, generalized eigenvalue problem and generalized singular value problem. The analogues are named as Weyl-type theorems.In applications,the perturbations are usually small. For such cases, we suggest anapproach to sharpen Weyl theorem.

1．引言对VOlterra弱奇异积分方程和积一微分方程之配置方法已有不少文章讨论［1－6］．由于其解在左端点处的非光滑性[3]并要得到m-1次多项式配置解的最优收敛率。，需采用所谓的等级网格．早期M作［1,2］是将等级指数r取为1，a表征核（t—s）ak（t，8）的奇异程度），但...

This paper deals with the numerical stability of block θ-methods for delaydifferential equations. We give the idea of PL-stability for numerical methods andthe necessary and sufficient conditions of PL-stability for block θ-methods.

We study a parallel Schwarz algorithm for the finite element approximationof obstacle problem in more general case. The convergence of the algorithm hasbeen established. The so-called finite step convergence for coincident componentsis discussed for problems of second order.

Bezier curve and Ball curve play an important role in CAGD. In this paper, weprovide conjugate basis of Ball basis in degree 2m + 1, by means of the conjugatebasis, we obtain Marsden equation in Ball basis. Transformation formula betweenBezier curve and Ball curve.

In this paper the trigonometric interpolation polynomial operators Fn(g; r, t)are constructed. Fn(g; r, t) converge the function g(t) on (-∞, ∞) uniformly if thefunction g(t) ∈ C2π. The convergence order is the best if g(t) ∈.j≤r (r≥1is nature number ).

In this paper we prove that the solutions of the finite element method for a classof parabolic equations converge to the solutions of the finite element method for aclass of elliptic equations as t→∞, this makes it available to get the numericalsolutions of elliptic equations by the difference schemes with intrinsic parallelismwhich initiated by professor Zhou Yulin.

In this paper, the elastic contact problems in which no friction is present andtheir linear finite element approximation have been considered. First the elasticcontact problems are classified intuitively according to the different location ofcontact boundary, and for one cases a new proof of existence of the solution ofproblem has been presented. Next a general error estimation of linear finite elementapproximation to the contact problem has been obtained under weaker assumptionfor the regularity of the solution of problem.

By introducing the concept of exceptional family discoved by G. Isac, we discussthe relation between the concept and the existence results in linear complementarityproblems. We not only recover many well known results, but also find a new resultrelating to G-matrix class. We also characterize, for the first time, the behavior ofthe multipliers in exceptional families. At last we propose an algorithm generattinga exceptional family, the algorithm has the property that it either finds a solutionof LCP or generates an exceptional family of LCP.

This paper proposes and discusses the solvability of the multidimensional totalleast perturbation problem in spectral normproves a necessary and sufficient condition for the solvability. The condition ismuch weaker than that of the multidimensional TLS problem.

In this paper, the convergence of segment explicit-implicit difference scheme forthe parabolic equation with discontinuous coefficients is discussed. The truncationerror of the difference scheme neighboring the points of discontinuity of the coefficients is O(1). It is shown that the solution of the difference scheme tends to thesolution of the differential equation in the sense of the maximum norm and therate of convergence is O(τ + ). Moreover, the numerical flux of the differencescheme tends to the flux of the differential equation in the mean, while the rate ofconvergence is O(τ + h).

This paper proves that, for complex polynomials, all extraneous fixed pointsfor any iteration of Halley iterative family and another relevant iterative family arerepelling. Thus no false convergent phenomenon arises on these iterations.

This paper concerns with measures of the sensitivity of a nondefective multiple generalized eigenvalue of a regular matrix-pair. Wilkinson condition numbers are introduced and some related properties are studied, especially, the Wilkinson's theorem on matrices with a very ill-conditioned eigenproblem is extended. A Gerschgorin-Weyl typed theorem is established. These results are useful to analyse the accuracy of computed eigenvalues.

In this paper,we discuss a Schwarz alternating method for a kind of unboundeddomains, which can be decomposed into a bounded domain and a half-planar domain. Finite Element Method and Natural Boudary Reduction are used alternatively. The uniform geometric convergence of both continuous and discrete problems is proved. The theoretical results as well as the numerical examples show thatthe convergence rate of this discrete Schwarz iteration is independent of the finiteelement mesh size, but dependent on the overlapping degree of subdomains.

In this paper, we consider multiplicative Schwarz algorithm for solving linear complementarity problems. Monotone convergence is obtained. under suitable conditions, we get the convergence independent of mesh size h. We also prove the finite termination property of the algorithm for the active constraints in noridegenerate case.

The convergence of maximum entropy methods is obtained on Kuhn-Tucker/Fritz John points. Then according to the nature of maximum entropy methods, we study the structure and convergent properties of feasible directions methods with nonmonotone curvilinear search rules from the unified point. On this basis, we discuss the numerically computing technique which combines nonmonotone curvilinear search methods and maximum entropy methods, and the numerically computing results for some optimization problems are obtained. The results show that our algorithm is efficient.

In this paper, we present a trust region algorithm for bound constrained minimization. Under milder conditions, we prove the global convergence of the main algorithm. It is also proved that the correct active set can be identified in a finite number of iterations if strict complementarity slackness condition holds, and so the proposed algorithm reduces finally to an unconstrained minimization method in a finite number of iterations, allowing a fast asymptotic rate of convergence.

This paper describes a numerical method for solving initial-boundary value problems of parabolic equations. Based on a representation of the Trotter product,we derive a new technigue for two-dimensional problems, which does not yield a large linear system, by using a splitting of the coefficient matrix. Furthermore,we prove that the proposed method, which is explicit, and unconditionally stable.Some numerical examples show that our method is superior to the Crank-Nicolson method.

The incompressible Navier-Stokes (INS) equations upon discretization on fixed meshes become a system of differential algebraic equations (DAE) of index 2. It is proved in this paper that for the general explicit and implicit Runge-Kutta (RK)methods, the time accuracy of velocity is the same as that for the ordinary differential equations, by taking into consideration of the special form of the resulting DAE; (the time accuracy of pressure can be lower). For the three-stage secondorder explicit RK method, algorithms with less (than three) Poisson solutions of pressure are proposed and verified by numerical experiments. However, in practical computation of complex flows it is found that the method must satisfy the so-called consistency condition for the components of the solution (here the velocity and the pressure) of the DAE for the method to be robust.

Consider DFP method for unconstrained optimization problems. Under some conditions, we prove the global convergence property of DFP method with Wolfe line search on uniformly convex objective function.

In this papert we discuss the inverse problem of 1-dimensional acoustic wave equation and propose an approximate inversion method, called multi-reflection elimination method, with which the approximate reflectivity function can be directly obtained by applying a certain transform to the response. The computation efforts for such method is only of the order N log N, much less than that of solving the direct problem, which is O(N2). On the basis of the proposed method, we also construct an iterative algorithm, and prove that the convergent order of iteration is two.

This paper is concerned with the numerical analysis of viscous-elastic flow problems relating material creep deformation nature under high temperature. Early works in this area are those by Barret, Liu[1], and Baranger and Najib [2]. These paper studied those model consisting only velocity and pressure as variables.Recently, in view of the special importance of the stress in material property,Baranger studied new finite element formula for quasi-Newtonian flow obeying power law, which consists stress, velocity and pressure as variables. Assume the Newtonian part is zero (see [3]), and one LBB condition is satisfied between the stress and velocity finite element spaces. Baranger has proven that the discrete formula has unique solution, and the error estimation is also deduced. Considering the restrictive condition given by [3] for finite element spaces, we can learn that it is difficult to use this method in practise.In this paper we constructs 4 new three field model, which also regards stress,velocity and pressure as variables, for above quasi-Newtonian flow problem, we also prove the existence and uniqueness of finite element solution, and deduce 'related error estimation, only by assuming a LBB condition hold between the velocity and pressure finite element spaces. Compared with that one in [3], the restrictive condition between velocity and stress finite element spaces is removed,thus we apparently relaxed the restrictive condition demanded to finite element space combination satisfying all our assumptions is proposed.

In this paper, we develop a two-level additive Schwarz preconditioner for Morley element using nonnested meshes. We define an intergrid transfer operator that satisfies certain stable approximation properties by using a conforming interpolation operator and construct a uniformly bounded decomposition for the finite element space. Both coarse and fine grid spaces are nonconforming. We get optimal convergence properties of the additive Schwarz algorithm that is constructed on nonnested meshes and with a not necessarily shape regular subdomain partitioning. Our analysis is based on the theory of Dryja and Widlund.It is interesting to mention that when coarse and fine spaces are all nonconforming, a natural intergrid operator seems to be one defined by taking averages of the nodal parameters. In this way, we obtain the stable factor (H/h)3/2, and show that this factor can not be improved. However, to get an optimal preconditioner,we need in general the stability with a factor C independent of mesh parameters.Therefore. the latter can not be used in this case.

The generalized Stein-Rosenberg type theorem is established for the parallel decomposition-type accelerated overrelaxation method (PDAOR-method) for solving the large scale block systems of linear equations. This thereby affords reliable criterions for judging the convergence and divergence, as well as the convergence rate and divergence rate, of this PDAOR-method.

In this paper, we concerns the sufficient conditions for the solubility of the mul tiplicative inverse eigenvalue problem. With the help of the topological mapping degree we give some new sufficient conditions, with improve some of de Oliveira's[2],He Xuchu and Dai Hua's[3] results.

This paper analyzes the influences of the deflation on the accuracy of the com pared eigenvalues of matrix. Based on the Rayleigh quotient theory, we proved that the influences, Generally speaking, are less important.

In this paper we discuss the stepwise collocation method for nonlinear volterra integral equation with multiple delays. It will be shown that, when the higher order interpolation operation is added to the numerical solutions generated by the continuous piecewise polynomial spline collocation with quasi-uniform meshes, the new approximate solutions will, under the appropriate assumptions, possess the optimal global superconvergence rates.