非定常不可压Navier-Stokes方程两重网格方法的稳定性和L2误差估计

讨论了二维非定常不可压Navier-Stokes方程的两重网格方法．此方法包括在粗网格上求解一个非线性问题,在细网格上求解一个Stokes问题．采用一种新的全离散(时间离散用Crank-Nicolson格式,空间离散用混合有限元方法)格式数值求解N-S方程．证明了该全离散格式的稳定性．给出了L2误差估计．对比标准有限元方法,在保持同样精度的前提下,TGM能节省大量的计算量．     

常微分方程组的整体解及两点边值问题——Ⅰ.整体解方法

众所周知,n维向量函数u(x)的一阶常微分方程组,如在某点上只给出n_1相似文献   

Numerical solution of integral equations in Chebyshev series

In this paper we discuss the Chebyshev series method with Newton iterations for the numerical solution of nonlinear integral equations. An existence theorem for nonlinear integral equations is given using a functional analytic approach. A method to compute and error bound to an approximate solution is discussed on the basis of the theorem.     

On a free interface problem for linear ordinary differential equations and the one-phase Stefan problem

A numerical method for the solution of the one-phase Stefan problem is discussed. By discretizing the time variable the Stefan problem is reduced to a sequence of free boundary value problems for ordinary differential equations which are solved by conversion to initial value problems. The numerical solution is shown to converge to the solution of the Stefan problem with decreasing time increments. Sample calculations indicate that the method is stable provided the proper algorithm is chosen for integrating the initial value problems.     

线性方程组的正解

讨论了线性方程组正解的若干性质,给出了线性方程组有正解的一个充要条件,以及由此得到的求正解的一般方法,还介绍了正解问题的若干应用.     

Global Minimization of Increasing Positively Homogeneous Functions over the Unit Simplex

In this paper we study a method for global optimization of increasing positively homogeneous functions over the unit simplex, which is a version of the cutting angle method. Some properties of the auxiliary subproblem are studied and a special algorithm for its solution is proposed. A cutting angle method based on this algorithm allows one to find an approximate solution of some problems of global optimization with 50 variables. Results of numerical experiments are discussed.     

A Geometrical Solution to a Tree Network Problem

A problem in tree networks, that of minimizing the cost of a pipeline tree connecting a source to a number of sinks, is discussed. A method of solution in which the optimal solution is synthesised from optimized subsystems is described. The method is built on the geometrical properties of the simplest subsystem; that with one source and two sinks. Experience with the method suggests that it is a practical alternative to numerical-iterative methods used hitherto.     

Artificial Monte Carlo interactions for solving some linear problems

A method of artificial interaction for Monte Carlo solution of ordinary differential equations with respect to probability measures is proposed. Under some conditions this method is advantageous over the standard method. A theoretical comparison of the complexity of the corresponding algorithms is provided. Also, results of numerical experiments are discussed.     

定常的Navier-Stokes方程的非线性Galerkin混合元法及其后验估计

提出了定常的Navier-Stokes方程的一种非线性Galerkin混合元法,并导出非线性Galerkin混合元解的存在性和误差估计及其后验误差估计.     

PLANE ELASTIC PROBLEMS OF DIFFERENT MEDIA WITH CRACKS ON THE INTERFACE

The equllibrium problem for the infinite elastic plane consisting of two different media with many cracks on the interface is discussed.It is transferred to a boundary value problem for analytic functions and then further reduced to a singular integral equation,the unique solvability and an effective method of solution for which are eatablished.A practical example in applications is illustrated,the solution of which is obtained in closed form.     

An accurate numerical solution for the transient heating of an evaporating spherical droplet

A recently derived numerical algorithm for one-dimensional time-dependent Stefan problems is extended for the purposes of solving a moving boundary problem for the transient heating of an evaporating spherical droplet. The Keller box finite-difference scheme is used, in tandem with the so-called boundary immobilization method. An important component of the work is the careful use of variable transformations that must be built into the numerical algorithm in order to preserve second-order accuracy in both time and space - an issue not previously discussed in relation to this widely-used scheme. In addition, we demonstrate that our solution is in close agreement with the solution obtained using an alternative numerical scheme that employs an analytic solution of the heat conduction equation inside the droplet, for which the droplet radius was assumed to be a piecewise linear function of time. The advantages of the new method are discussed.     

Estimating a reduced rank regression model for non-normal variables

A method using third order moments for estimating the regression coefficients as well as the latent state scores of the reduced-rank regression model when the latent variable(s) are non-normally distributed is presented in this paper. It is shown that the factor analysis type indeterminacy of the regression coefficient matrices is eliminated. A real life example of the proposed method is presented. Differences of this solution with the reduced-rank regression eigen solution are discussed.     

A fractal Boussinesq equation for nonlinear transverse vibration of a nanofiber-reinforced concrete pillar

An approximate Hamilton principle is established for the transverse vibration of a reinforced concrete pillar by considering the dissipation energy, and a generalized Boussinesq equation is obtained. The exp-function method is adopted to solve the equation, and its solution properties are discussed and elucidated, including solitary solution, blowup solution, and discontinuous solution. In order to study the effect of a porous structure on the vibration property, fractal calculus is used to derive the fractal Boussinesq equation, and a fractal variational principle is also established. The fractal model confers many attractive properties, which can not be revealed by the traditional protocol. The effect of the nanofiber-reinforced concrete structure on its wave morphology is discussed and illustrated. A blowup solution can be converted into a flat solution by adjusting the value of the fractal derivative order. The paper sheds new light on the design of reinforced concrete pillars to avoid vibration damage.     

Development of some cutting stock algorithms

A multivariant scheme of the south-eastern angle method for a two dimensional mass cutting stock problem is discussed in the paper. The use of a flexible linear programming package LP-LGIT for the solution of such problems with various column generators is described. The paralleling of a computational scheme of the method of the generating structures is suggested.     

奇摄动问题中脉冲状解的“缝接法”

讨论了一类含有脉冲状解的奇摄动边值问题.由于这类问题自身的不稳定性而无法采用微分不等式方法.利用边界层函数法构造了形式渐近解,并运用"缝接法"证明了问题解的存在性以及进行了余项估计.     

Numerical solution for a nonlinear,one-dimensional problem of thermoelasticity

A numerical solution for a nonlinear, one-dimensional boundary-value problem of thermoelasticity for the elastic half-space is presented. The resulting equations are discussed and the numerical method is investigated for stability. Comparison with other existing numerical schemes is carried out. The obtained results clearly indicate the process of shock formation. The presented figures show the effects of different nonlinear coupling constants on the distributions of the mechanical displacement and temperature in the medium. A special case is briefly discussed.     

Error behaviour of multistep methods applied to unstable differential systems

The problem of modelling a dynamic system described by a system of ordinary differential equations which has unstable components for limited periods of time is discussed. It is shown that the global error in a multistep numerical method is the solution to a difference equation initial value problem, and the approximate solution is given for several popular multistep integration formulae. Inspection of the solution leads to the formulation of four criteria for integrators appropriate to unstable problems. A sample problem is solved numerically using three popular formulae and two different stepsizes to illustrate the appropriateness of the criteria.     

On the explicit parametric description of waves in periodic media

A method for the parameterization of the one-dimensional wave equation is proposed that makes it possible to find its solution by quadratures under an arbitrary dependence of the refraction index on the current wave phase. The form of the solution found is used to investigate the structure of the wave function for a periodic refraction index. Explicit expressions for the fundamental system of solutions and for the Floquet index are obtained. Examples of applying the proposed method to the optimal synthesis of multilayer interference mirrors and Bragg waveguides are discussed.     

Determination of the optimal initial function and the parameters in a system described by delay-differential equations

The determination of the initial function and the parameters in a system of delay-differential equations minimizing a cost functional is considered. The existence of a solution to the problem is discussed. A set of necessary optimality conditions is derived, and a computational method is presented to obtain a locally minimal solution.     

On nonlinear time-dependent multivelocity transport equations

The aim of this paper is to show the existence and uniqueness of a solution for a class of nonlinear multivelocity neutron transport equations and to present a method for the determination of the solution. A recursion formula for the construction of a solution by the method of successive approximations and an error estimate for approximate solutions are given. Both global and local solutions are discussed. The conditions imposed on the nonlinear equation are directly applicable to the linear multivelocity transport problem, and a recursion formula for this system is also given. In the process of approximations, only successive integrations are involved. This fact indicates a promising possibility for the calculation of numerical results by using a computer. A brief discussion of this possibility and the applicability of the results on nonlinear problems are included.