中国科学院数学与系统科学研究院期刊网

计算数学 2000年 22卷

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1. 均匀格子气Boltzmann方程的稳定性研究
孙成海,史俊杰
计算数学    2000, 22 (1): 1-12.   DOI: 10.12286/jssx.2000.1.1
摘要1189)      PDF(pc) (493KB)(663)    收藏
The Lyapunov method is applied to finite difference equations in order to study the stability and asymptotic properties of Boltzmann equation of lattice gas. The existence and uniqueness of the equilibrium state are proved. A Lyapunov function can be formed by means of function H that is decreasing and takes its minimum value at the equilibrium state. By the Lyapunov function the stability is Obtained. Moreover, a sufficient condition is provided that makes the function H strictly decrease except at the equilibrium state. The asymptotic stability for homogeneous Boltzmann equation of lattice gas is proved under this condition.
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2. 一般线性方法的线性与非线性稳定性间的关系
阮保庚
计算数学    2000, 22 (1): 13-20.   DOI: 10.12286/jssx.2000.1.13
摘要1212)      PDF(pc) (349KB)(734)    收藏
Some new concepts of stability are introduced for general linear methods, and algebraic conditions for stability of the methods are proposed which are suitable not only for implicit methods but also for explicit methods. Our results characterize the interrelation between linear and nonlinear stability so that new evidence for the construction of efficient and stable methods is offered.
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被引次数: Baidu(2)
3. 一般线性方法的正则性
黄乘明,肖爱国
计算数学    2000, 22 (1): 21-28.   DOI: 10.12286/jssx.2000.1.21
摘要1148)      PDF(pc) (257KB)(700)    收藏
In this paper, the concepts of regularity and strong regularity of general. linear methods are introduced. We investigate the conditions which guarantee that general linear methods preserve asymptotic values of the systems of ordinary differential equations. This work extends the existed results of Runge-Kutta methods and linear multistep methods.
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被引次数: Baidu(6)
4. 一类双对称矩阵反问题的最小二乘解
谢冬秀,张磊,胡锡炎
计算数学    2000, 22 (1): 29-40.   DOI: 10.12286/jssx.2000.1.29
摘要1185)      PDF(pc) (350KB)(1000)    收藏
A=(a_ij) ∈R~(n×n ) is termed bisymmetric matrix if We denote the set of all n × n bisymmetric matrices by BSR~(n×n ) In this paper, we discuss the following two problems: Problem I. Given X, Find such that Problem Ⅱ. Gived . Find such that where ||·|| is Frobenius norm, and S_E is the solution set of Problem I. The general form of S_E has been given. The necessary and sufficient conditions have been studied for the special cases AX = B and AX = XA of problem I. For problem Ⅱ the expression of the solution has been provided.
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被引次数: Baidu(336) CSCD(27)
5. 形状记忆合金问题的有限元逼近
程晓良,叶兴德
计算数学    2000, 22 (1): 41-48.   DOI: 10.12286/jssx.2000.1.41
摘要1347)      PDF(pc) (238KB)(746)    收藏
In this paper discrete approximations are discussed to a nonlinear evolutionary system of partial differential equations arising from modelling the structural transitions in shape memory alloy. The existence and uniqueness of the discrete solutions are proved and error estimates for the fully discrete scheme are derived.
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被引次数: Baidu(5)
6. 带对流项的渗流型方程的显格式
朱少红,袁光伟,沈隆钧
计算数学    2000, 22 (1): 49-58.   DOI: 10.12286/jssx.2000.1.49
摘要1139)      PDF(pc) (344KB)(674)    收藏
In this paper, the difference method for the equation of filtration type with convection is considered. The explicit scheme with artificial viscosity is given, then the convergence of the difference solution is proved by the method of discrete functional analysis. Meanwhile, the existence of the weak solution of the differential equation is obtained. At last, the numerical examples reveal the important properties of the solution to the equation of filtration type.
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被引次数: CSCD(1)
7. 解第一类边界积分方程的高精度机械求积法与外推
吕涛,黄晋
计算数学    2000, 22 (1): 59-72.   DOI: 10.12286/jssx.2000.1.59
摘要1542)      PDF(pc) (442KB)(768)    收藏
By means of Side-Israeli's quadrature reules, quadrature methods for solving boundary integral equations of the first kind are presented, which have high accuracy O(h~(3)). Moreover, the asymptotic expansions with the odd pwoers h~(2μ-1) (μ= 2, 3) of the errors are shown, that is, using extrapolations, we can improve the accuracy order of approximations..
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被引次数: Baidu(42) CSCD(7)
8. 对称Toeplitz系统的快速W变换基预条件子
成礼智
计算数学    2000, 22 (1): 73-82.   DOI: 10.12286/jssx.2000.1.73
摘要1166)      PDF(pc) (397KB)(959)    收藏
A new matrix algebra W, including the set of real symmetric skewcirculant matrices, is introduced. It is proved that all the matrices of W can be simultaneously diagonalized by the discrete W transform matrix. As an application, the use of preconditioned iterative method (preconditioner W1_(T_n) belongs to matrix class W) to solve a system of equations with a Toeplitz coefficients matrix is developed. If generating function f(x) is nonnegative piecewise continuous and has enumerable zero points, we conclude that the spectrum of iterative matrix have a cluster at one. The results of numerical tests with this preconditioner are presented.Our preconditioner is comparable, and if f(x) is not smooth that superior, to Strang's circulant preconditioner and Huckle's skewcirculant preconditioner.
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被引次数: Baidu(14) CSCD(3)
9. 多孔介质驱动问题的混合元最小二乘特征有限元方法及其收敛分析
赵卫东
计算数学    2000, 22 (1): 83-96.   DOI: 10.12286/jssx.2000.1.83
摘要1190)      PDF(pc) (485KB)(669)    收藏
The mathematical model for two-phase displacement in porous media is a coupled initial boundary value problem of nonlinear partial differential equations which consist of a pressure equation and a saturation equation. In this paper, the mixed least-square weak form of pressure equation is got, and the positive definite characteristics of the weak form is proved. Based on this weak form, a new kind of numerical methods for two-phase displacement problems is proposed: the mixed least-square finite element method is used to solve pressure and Darcy velocity, and the saturation is solved by using characteristic finite element method. The main merits of the mixed least-square finite element method compared with mixed finite element method are: first, the structure of the mixed least-square finite el- ement spaces is just standard finite element spaces, it is simple and easy to use; second, the weak form of the mixed least-square finite element method for pressure is symetric and definite positive, thus there are many efficient methods to solve numerically; and the last, the Darcy velocity solved by mixed least-square finite element method is continuous. In numerical analyses, a very important inequality is obtained which is used to control the errors of the pressure and Darcy velocity, and the optimal error estomates of the proposed method are proved.
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被引次数: Baidu(1)
10. 一类非协调元的收敛性分析
石钟慈,王家城
计算数学    2000, 22 (1): 97-2.   DOI: 10.12286/jssx.2000.1.97
摘要1143)      PDF(pc) (202KB)(632)    收藏
In this paper, two nonconforming finite elements are discussed. They pass the generlized patch test and can be used in the numerical solution of second order elliptic problems.
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被引次数: Baidu(38) CSCD(5)
11. 一类非线性反应扩散方程组的有限元分析
江成顺,崔霞
计算数学    2000, 22 (1): 103-112.   DOI: 10.12286/jssx.2000.1.103
摘要1377)      PDF(pc) (365KB)(767)    收藏
This paper is concerned with the finite element scheme and the alternating direction finite element scheme for some nonlinear reaction - diffusion systems with the second or the third boundary value conditions. Not only the existence and uniqueness of solutions for these approximational schemes are obtained, but also the optimal H~(1) - norm and L~(2)- norm error estimate results are demonstrated.
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被引次数: Baidu(70) CSCD(1)
12. 一类广义插值函数与广义有限元方法的后验估计
舒适,黄云清,喻海元
计算数学    2000, 22 (1): 113-120.   DOI: 10.12286/jssx.2000.1.113
摘要1528)      收藏
In this paper, we discuss a generalized finite element interpolation problem and obtain the asymptotic expansion of the interpolation function. Based on these results, the error asymptotic expansion and superconvergence result of the generalized finite element approximation are derived. Finallym using the Superconvergent Patch Recovery Technique (SPR) proposed by Zienkiewicz & Zhu, we get the superconvergent recovery approximation and the posteriori error estimates to the flux. The numerical test convinced our analysis.
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被引次数: Baidu(19) CSCD(1)
13. 调和方程第一边值问题高效概率算法
朱起定
计算数学    2000, 22 (1): 121-128.   DOI: 10.12286/jssx.2000.1.121
摘要1199)      收藏
In this paper, a new probabilistic computing mehtod for the first harmonic boundary value problem are obtained by a new way to solve trasfer matrix equations. At last, some numerical examples are given.
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被引次数: Baidu(32) CSCD(7)
14. 线性流形上双对称阵逆特征值问题
张磊,谢冬秀,胡锡炎
计算数学    2000, 22 (2): 129-138.   DOI: 10.12286/jssx.2000.2.129
摘要1263)      PDF(pc) (304KB)(733)    收藏
A = (aij) R~n×n is termed bisymmetric matrix if We denote the set of all n×n bisymmetric matrices by BSR~(n×n) Let Where when n =2k, and n = 2k+1, In this paper, we discuss the following two problems: Problem Ⅰ. Given X R~n×m, B R~n×m. Find A S such that Problem Ⅱ. Given A* E R~n×n. Find A S_E such that Where is Frobenius norm, and S_E is the solution set of Problem I. In this paper the general representation of S_E has been given. The necessary and sufficient conditons have been presented for Problem I_0. For Problem Ⅱ the expression of the solution has been provided.
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被引次数: Baidu(163) CSCD(8)
15. 非线性抛物组非均匀网格差分解的唯一性和稳定性
袁光伟
计算数学    2000, 22 (2): 139-150.   DOI: 10.12286/jssx.2000.2.139
摘要1195)      PDF(pc) (349KB)(729)    收藏
In this paper the uniqueness and stability of the difference solutions with nonuniform meshes for the nonlinear parabolic system are proved.
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被引次数: Baidu(21) CSCD(3)
16. W空间中有界线性算子的最佳逼近及其应用
文松龙,金昌录,朴东哲
计算数学    2000, 22 (2): 151-158.   DOI: 10.12286/jssx.2000.2.151
摘要1159)      PDF(pc) (280KB)(802)    收藏
In this paper, we give the best approximating A. for { (xi, yi) [c, d] of following form of bounded linear operator A in the space W, and discussed convergences of An. We also give the numerical solution of linear operator equation (An) (x, y) = f(x, y) for application.
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被引次数: Baidu(18)
17. 二维非线性对流扩散方程的非振荡特征差分方法
由同顺
计算数学    2000, 22 (2): 159-166.   DOI: 10.12286/jssx.2000.2.159
摘要1126)      PDF(pc) (320KB)(677)    收藏
The nonosillatory characteristic diffeence method for the nonlinear convectiondiffusion equation in 2D is discussed in the paper. We constructed quadratic UNO and ENO interpolations based on six mesh points in 2D. Combing them with characteristic difference method, we establish the high-resolution difference schemes for the nonlinear convection-dominated diffusion problem. Because theses schemes are nonlinear inherently, we use a new method to give the strict error analyses of these schemes, solving the difficulties resulted from the nonlinearity. The numerical computation is given in the paper for the model problem.
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被引次数: Baidu(36) CSCD(5)
18. 方程u_(tt)=u_(xxt)+f(u_x)_x初边值问题的差分法
高兴宝 ,万桂华 ,陈开周
计算数学    2000, 22 (2): 167-176.   DOI: 10.12286/jssx.2000.2.167
摘要1235)      PDF(pc) (323KB)(878)    收藏
The finite difference method is considered for.the following initial-boundary- Value problem: where j(s), (x) and (x) are given functions; QT = [0, 1]× [0, T]. The convergence of the finite difference schemes is verified by discrete functional analysis methods and prior estimation techniques.
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被引次数: Baidu(38)
19. 非均匀分形插值函数的光滑性和Hlder指数
卢建朱
计算数学    2000, 22 (2): 177-182.   DOI: 10.12286/jssx.2000.2.177
摘要1273)      PDF(pc) (189KB)(764)    收藏
In this paper we consider the smoothness of fractal interpolation functions on a general set of nodes, and obtain the estimation of its Hlder exponent.
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20. 离散速度动力学方程组的数值方法研究 Ⅰ.半隐式差分格式
汤华中,邬华谟
计算数学    2000, 22 (2): 183-190.   DOI: 10.12286/jssx.2000.2.183
摘要1298)      PDF(pc) (254KB)(907)    收藏
This paper is to study the numerical approximations of the discrete-velocity kinetic equations (DVKE). We analyze the nonlinear stability, such as TV stability, L stability, for the semi-implicit difference schemes applied to DVKEs. Furthermore, the numerical entropy condition for a special difference scheme is also considered.
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21. 多级系统可靠性最优化的分解对策模型及其协调算法
高作峰
计算数学    2000, 22 (2): 191-196.   DOI: 10.12286/jssx.2000.2.191
摘要1205)      PDF(pc) (256KB)(779)    收藏
For a multilevel engineering system, considering reliabilities as decomposition parameters, construction costs as coordination parameters, its decomposition models for reliability optimization is constructed, and its corresponding coordination algorithm is also given.
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22. 关于外梯度法的步长规则
修乃华,王长钰
计算数学    2000, 22 (2): 197-208.   DOI: 10.12286/jssx.2000.2.197
摘要1270)      PDF(pc) (458KB)(861)    收藏
It is known that stepsize's choice plays a key role in convergence and efficiency of the extragradient method, which is a special projection-type method, for solving monotone variational inequality problems. In this paper, by analyzing the existing stepsize rules, a predictor stepsize rule without the bounded restriction is proposed, and a corrector stepsize rule with (approximate) optimality is also presented. The corresponding convergence properties and numerical examples are shown.
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被引次数: Baidu(16) CSCD(1)
23. 数值求解Euler方程的UCGVC差分格式的注记
朱庆勇,李岳生
计算数学    2000, 22 (2): 209-218.   DOI: 10.12286/jssx.2000.2.209
摘要1260)      PDF(pc) (405KB)(803)    收藏
A high order accurate finite difference scheme (UCGVC) for solving the Euler equations is described in this paper. The flux vectors in Euler equations are split by using Sieger-Warming's flux vectors splitting technique[1]. The flux vectors are approxunated by using upwind compact scheme[2]. In order to preyed the nonphysical oscillations in the vicinity of the shock the group velocity control method is used.
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被引次数: Baidu(5) CSCD(2)
24. 轴对称渗流中自由边界问题的近似解法
许作良,张关泉
计算数学    2000, 22 (2): 219-226.   DOI: 10.12286/jssx.2000.2.219
摘要1833)      收藏
In this paper, we discuss a free boundary problem occurring in axisymmetric filtration with nonhomogeneous anisotropic medium, which can be transformed into a mixed boundary value problem for nonlinear elliptic complex equations. By using Newton imbedding method, approximate solutions of the mixed boundary Value problem are obtained, and if proper conditions hold, we have also given error estimates of the approximate solutions.
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25. 二维Helmholtz方程外问题基于自然边界归化的非重叠型区域分解算法
余德浩,贾祖朋
计算数学    2000, 22 (2): 227-240.   DOI: 10.12286/jssx.2000.2.227
摘要2134)      收藏
In this paper, based on natural boundary reduction suggested by Feng and Yu, an nonoverlapping domain decomposition method with its discretization is presented for the exterior problem of 2-D Helmholtz equation. The convergence of the D-N alternating algorithm and its discretization are studied. Some numerical results are given.
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被引次数: Baidu(75) CSCD(9)
26. 抛物问题的拉格朗日乘子区域分解法
胡齐芽,梁国平,孙澎涛
计算数学    2000, 22 (2): 241-256.   DOI: 10.12286/jssx.2000.2.241
摘要1455)      收藏
In this paper we consider domain decomposition methods with Lagrangian multipliers, which are applied to solving parabolic problems. We shall estimate condition numbers of the resulting interface matrices, and construct two kinds of simple preconditioners for the corresponding interface equations. It will be shown that the condition numbers of the resulting preconditioned interface matrices are almost optimal.
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被引次数: CSCD(1)
27. 铁磁链Landau-Lifshitz方程的显式差分法
万桂华
计算数学    2000, 22 (3): 257-264.   DOI: 10.12286/jssx.2000.3.257
摘要1255)      PDF(pc) (353KB)(830)    收藏
In this paper, the Landau-Lifshitz equation with periodic initial boundary val- ued problem which is govnered by ■μ/■t=-α_1μ×(μ×Δμ)+α_2(μ×Δμ) is discreted by using the Euler-forword finite difference method. The proposed scheme is explicit so that the parallel algorithm can be used to simulate numerically on computer. Moreove, the convergence and stability of the proposed scheme are proved by the finite extensive method of the nonlinear function. Finally, the numerical experiments are provided to check the theoritical results.
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28. 反演声波阻尼系数的一个逼近方法
王连堂
计算数学    2000, 22 (3): 265-274.   DOI: 10.12286/jssx.2000.3.265
摘要1204)      PDF(pc) (320KB)(859)    收藏
The inverse time-hormonic acoustic scattering problem we are considering in this paper is to recover the impedance coefficient from the far field pattern of the scattered wave.An approximation method is presented and the conversgence of this method is proven.Numerrical examples are given showing that this method is both accurate and simple to use.
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被引次数: Baidu(42) CSCD(5)
29. 由两点确定的具凸包性和保凸性的三次有理Bézier曲线
潘日晶
计算数学    2000, 22 (3): 275-284.   DOI: 10.12286/jssx.2000.3.275
摘要1191)      PDF(pc) (446KB)(677)    收藏
This paper shows that under a necessary and sufficient condition, there exists a cubic rational Bezier curve with convex hull property and convexity preserving property which passes two given points inside the control polygon.
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被引次数: Baidu(5)
30. 一类自适应的单块法及其变步长实现方案
张国凤,赵双锁
计算数学    2000, 22 (3): 285-294.   DOI: 10.12286/jssx.2000.3.285
摘要1171)      PDF(pc) (433KB)(774)    收藏
This paper presents a class of self-staring-type A-stable implicit one-block method with stepsize control for solving stiff ODEs initial value problems on paral- lel computers;gives also its algorithms and implementation strategy with varying stepsize.Theoretical analysis and numerical tests indicate that this one-block method is efficient for solving Stiff ODEs initial value problems.
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被引次数: Baidu(7)
31. 非协调板元的一般性误差估计式
陈绍春,石东洋
计算数学    2000, 22 (3): 295-300.   DOI: 10.12286/jssx.2000.3.295
摘要1412)      PDF(pc) (239KB)(915)    收藏
Suppose the solution and load , with a modified discrete equation, we give the error estimate: which can be applied to almost known nonconforming plate elements.
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被引次数: Baidu(37) CSCD(5)
32. 板问题多重网格法收敛性的低模估计
许学军,邓庆平
计算数学    2000, 22 (3): 301-308.   DOI: 10.12286/jssx.2000.3.301
摘要1428)      PDF(pc) (262KB)(810)    收藏
In this paper, we obtain H1 norm estimate for multigrid method for plate bending problem. Meanwhile, optimal convergence rate under H1 norm is also obtainted for nested iteration multigrid method.
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被引次数: Baidu(5)
33. 对流扩散方程的经济差分格式
程爱杰,赵卫东
计算数学    2000, 22 (3): 309-318.   DOI: 10.12286/jssx.2000.3.309
摘要1230)      PDF(pc) (420KB)(893)    收藏
An economical difference scheme is proposed to solve convection-diffusion equations. The transport term is discretized by the method of characteristics, then the difference system are docomposed to several problems of individual variable using alternating direction method. Two kinds of interpolation operators are supplied for the technique of characteristics. The stability and convergence are analysed by energy method. Numerical result implies that this scheme has better accuracy and higher efficiency then the standard scheme of two-order center difference quotient.
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被引次数: Baidu(99) CSCD(11)
34. 组合RK-Rosenbrock方法及其稳定性分析
陈丽容,刘德贵
计算数学    2000, 22 (3): 319-332.   DOI: 10.12286/jssx.2000.3.319
摘要1331)      PDF(pc) (435KB)(673)    收藏
This paper deals with a class of combined RK- Rosenbrock (CRKR) methods for a partitioned system of stiff differential equations based on the parallelism across the system. Nonstiff subsystem is integrated by a explicit RK method while a Rosenbrock method is used for the stiff subsystem. The paper discusses numerical stability, and the numerical tests are conducted on a multiprocessor system.
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被引次数: CSCD(1)
35. 紧支撑正交对称和反对称小波的构造
杨守志,杨晓忠
计算数学    2000, 22 (3): 333-338.   DOI: 10.12286/jssx.2000.3.333
摘要1242)      PDF(pc) (245KB)(773)    收藏
The objective of this paper is to exhibit the construction of compactly supported orthonormal symmetric scaling functions with scaling factor a=4 and the three corresponding compactly supported orthonormal wavelets,one of which is symmetric and the others are antisymmetric. The orthonormal wavelets of L2(R) isn't unique. It is possible to choose "good" base from a lot of wavelets base. Examples of scaling functions and wavelets are given.
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被引次数: Baidu(33) CSCD(6)
36. 一个第二类变分不等式的有限元逼近
王烈衡
计算数学    2000, 22 (3): 339-344.   DOI: 10.12286/jssx.2000.3.339
摘要1193)      PDF(pc) (175KB)(744)    收藏
The finite element methods for the second type variational inequality deduced from the simplified contact problem with friction have been considered by R.Glowinski et al [2]. In this note, the modified finite element method with numerical integration for this problem is considered, and the error estimate is improved.
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被引次数: Baidu(16) CSCD(1)
37. 由主子阵和缺损特征对构造Jacobi矩阵
胡锡炎,张磊,彭振赟
计算数学    2000, 22 (3): 345-354.   DOI: 10.12286/jssx.2000.3.345
摘要1212)      收藏
This paper considers the problem of constructing a Jacobi matrix from its defec tive eigen-pair and a principal submatrix. Some necessary and sufficient conditions of solvability have been derived. An algorithm and two numerical examples have been given.
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被引次数: Baidu(48) CSCD(5)
38. 椭圆外区域上的自然边界元法
邬吉明,余德浩
计算数学    2000, 22 (3): 355-368.   DOI: 10.12286/jssx.2000.3.355
摘要1919)      收藏
In this paper we discuss the natural boundary element method for harmonic equation in an exterior elliptic domain. By studying the properties of the natural integral operator and the Poisson integral operator, we develop a numerical method to solve the natural integral equation. We also devise a fast algorithm for the solution of the corresponding system of linear equations. Finally we present some numerical results.
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被引次数: Baidu(62) CSCD(15)
39. 非拟牛顿非凸族的收敛性
陈兰平,焦宝聪
计算数学    2000, 22 (3): 369-378.   DOI: 10.12286/jssx.2000.3.369
摘要1201)      收藏
In this paper, the non-quasi-Newton's family is investigated. A class of inexact linesearch procedures are used, which are combined with the non-quasi-Newton's family. We study the global convergence properties of the non-quasi-Newton's family, when applied to a convex objective function. We show global and superlinear convergence for this class methods on uniformly convex objective function.
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被引次数: CSCD(2)
40. 正定可对称化矩阵与预对称迭代算法
孙家昶
计算数学    2000, 22 (3): 379-384.   DOI: 10.12286/jssx.2000.3.379
摘要1226)      收藏
Second order elliptic equation is a class of mathematical model for scientific computing, such as convex-diffusion, oil-reservoir simulation, etc. Based on intrinsic symmetrizable property, a new concept on positively symmetrizable matrix is proposed in this paper. We point that for such kind of equation systems, it is possible to adopt special preconditioning CG algorithm, e.g. [1]-[3], instead of the usual iteration procedure for general non-symmetry systems, such as GMRES [3]-[4] ) BiCGSTAB [5]. Numerical tests show the new algorithm is effective for solving this kind of second order elliptic discrete systems.
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被引次数: Baidu(59) CSCD(3)