Convergence theorem of common fixed points for Lipschitzian pseudo-contraction semi-groups in Banach spaces

The purpose of this paper is to study the weak convergence problems of the implicity iteration process for Lipschitzian pseudocontractive semi-groups in the general Banach spaces. The results presented in this paper extend and improve the corresponding results of some people.     

Shock wave solution of the Boltzmann kinetic equation in a 13-moment approximation

We consider the classic problem of a one-dimensional steady shock-wave solution of the Boltzmann kinetic equation utilizing a new type of 13-moment approximation proposed by Oguchi (1997). The model, unlike previous ones, expresses the collision term in an explicit function of the molecular velocity. This enables us to examine directly the nature of the singularity of the distribution function to this particular problem caused by the vanishing molecular velocity. We can thus obtain moment integrals directly because of its explicit expression. The principal value is utilized for the moment integral to cope with the singularity, and we can have five relations for five unknown functions to be determined with respect to the coordinate x. These relations can be reduced to a first-order differential equation that is solved to provide the familiar smooth monotonic transition from the upstream supersonic state to the subsonic downstream state. Computed values of shock thickness for various shock Mach numbers agree well with existing results obtained by different methods to the certain Mach number beyond which no solution exists.Received: 17 May 2002, Accepted: 1 May 2003, Published online: 15 August 2003PACS: 51.10. + y     

ON PROBLEM OF NEAREST COMMON FIXED POINT OF NONEXPANSIVE MAPPINGS

The purpose is by using the viscosity approximation method to study the convergence problem of the iterative scheme for an infinite family of nonexpansive mappings and a given contractive mapping in a reflexive Banach space. Under suitable conditions, it was proved that the iterative sequence converges strongly to a common fixed point which was also the unique solution of some variational inequality in a reflexive Banach space. The results presented extend and improve some recent results.     

Spectral galerkin approximation of couette-taylor flow

Axisymmetric Couette-Taylor flow between two concentric rotating cylinders was simulated numerically by the spectral method. First, stream function form of the Navier-Stokes equations which homogeneous boundary condition was given by introducing Couette flow. Second, the analytical expressions of the eigenfunction of the Stokes operator in the cylindrical gap region were given and its orthogonality was proved. The estimates of growth rate of the eigenvalue were presented. Finally, spectral Galerkin approximation of Couette-Taylor flow was discussed by introducing eigenfunctions of Stokes operator as basis of finite dimensional approximate subspaces. The existence, uniquence and convergence of spectral Galerkin approximation of nonsingular solution for the steady-state Navier-Stokes equations are proved. Moreover, the error estimates are given. Numerical result is presented.     

Iterative solution of the dynamic responses of locally nonlinear structures with drift

Considering the operating point drift in the dynamic responses of locally nonlinear structures, a new iterative method based on describing functions is introduced to solve for the steady-state frequency response. Drift in the operating point arises in the presence of asymmetric nonlinearity, pre-deformation or static loads. In this study, the internal nonlinear forces are expressed using describing functions. The complex equations governing the responses of multiple frequency components are established and are iteratively solved using the Inverse Matrix Update Method. The nonlinear frequency responses can thus be rapidly obtained, and the validity of the method is verified by simulations. The presented method can be applied to large-scale structures with multiple nonlinear elements.     

One approximate solution of the Nekrasov problem

An approximate solution ω = A[ω, μ] of the nonlinear integral Nekrasov equation is obtained by successive replacement of the kernel of the integral operator by a close one. The solution is sought not directly at the bifurcation point μ₁ = 3 of the linearized equation ω = μL[ω] but at the point μ = 1 at which operator A[ω, μ], remaining nonlinear in ω, is linear in μ. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 50–56, November–December, 2007.     

General solution of multi-valued displacement problem of an eccentric circular ring

In this paper, by using N.I, Muskhelishvili’s method a multi-valued displacement problem is considered for an eccentric circular ring. The general expression of stress function is derived in the bipolar coordinate system and its application is explained.     

On the Mann and Ishikawa iterative approximation of solutions to variational inclusions with accretive type mappings in Banach spaces

The purpose of this paper is to introduce and study the existence of solutions and convergence of Mann and Ishikawa iterative processes for a class of variational inclusions with accretive type mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results by Chang, Ding, Hassouni, Kazmi, Siddiqi, Zeng et al. Foundation item: the National Natural Science Foundation of China (19771058)     

Mann and Ishikawa iterative approximation of solutions form-accretive operator equations

The purpose of this paper is to study the Mann and Ishikawa iterative approximation of solutions for m-accretive operator equations in Banach spaces. The results presented in this paper extend and improve some authors’ recent results.     

Iterative approximation with errors of fixed point for a class of nonlinear operator with a bounder range

Let X be a uniformly smooth real Banach space. Let T:X → X be continuos and strongly accretive operator. For a given f ε X, define S: X → X by Sx =f−Tx+x, for all x ε X. Let {a_n} _n=0 ^∞ , {β_n} _n=0 ^∞ be two real sequences in (0, 1) satisfying:

Large deformation solution of stiffened plates by a mixed finite element method

In the present paper, a finite element mixed variational functional and the iterative equations of the eccentric orthogonal stiffened plates are developed in accordance with nonlinear elasticity. By using an important technique the coupling coefficients of the two-dimensional coupling matrix are resolved into the known input data in the programming which is a three-dimensional coefficient matrix. The nonlinear equations are transformed into the instantaneous linear equations; and by using the conjugate gradient method the linear equations are solved. As a result, therefore, the calculation is enormously simplified, the precision manifested, and a satisfactory result obtained.     

Mikusinski’s operators solution of three-order linear difference equation with variable coefficients

This paper proceeds the papers [3] [4], we make use of the idea of the variable number operators and some concepts and conclusions of the shifting operators series with variable coefficients in the operational field of Mikusinski, it is devoted to the solution of the general three-order linear difference equation with variable coefficients, and it is also devoted to the better solution formula for the some special three-order linear difference equations with variable coefficients: in addition, we try to provide the idea and method for realizing solution of the more than three-order linear difference equation with variable coefficients. Project Supported by the Science Foundation of Anhui Province     

ON THE ITERATIVE APPROXIMATION PROBLEM OF FIXED POINTS FOR ASYMPTOTICALLY NONEXPANSIVE TYPE MAPPINGS IN BANACH SPACES

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｒｏｕｇｈｏｕｔｔｈｉｓｐａｐｅｒｗｅａｓｓｕｍｅｔｈａｔＥｉｓａｒｅａｌＢａｎａｃｈｓｐａｃｅ ,Ｅ ｉｓｔｈｅｄｕａｌｓｐａｃｅｏｆＥ ,ＤｉｓａｎｏｎｅｍｐｔｙｓｕｂｓｅｔｏｆＥａｎｄＪ:Ｅ → 2 Ｅ ｉｓｔｈｅｎｏｒｍａｌｉｚｅｄｄｕａｌｉｔｙｍａｐｐｉｎｇｄｅｆｉｎｅｄｂｙＪ(ｘ) =ｆ∈Ｅ :〈ｘ ,ｆ〉 =‖ｘ‖·‖ｆ‖ ,　‖ｆ‖ =‖ｘ‖ (ｘ∈Ｅ) .　　Ｄｄｆｉｎｉｔｉｏｎ 1 1　ＬｅｔＴ :Ｄ →Ｄｂｅａｍａｐｐｉｎｇ1 )Ｔｉｓｓａｉｄｔｏｂｅａｓｙｍｐｔｏｔｉｃａｌｌｙｎｏ…     

A rigorous solution for the axisymmetrical buckling of simply supported cylindrical sandwich shells under axial load

In this paper,based on ref[1],the axisymmetrical buckling of simply supportedcylindrical sandwich shells under the action of uniform axial load is solved by a rigorousmethod.The classical theory of shells is used for the two face sheets and the core isconsidered as a three-dimensional elastic body.A series of transcendental equations areobtained,from which the critical loads can be calculated by numerical methods.Numericalexamples are given to compare with the solutions of sandwich shell theories.     

Comparison of Iterative Methods for Computing the Pressure Field in a Dynamic Network Model

In dynamic network models, the pressure map (the pressure in the pores) must be evaluated at each time step. This calculation involves the solution of a large number of nonlinear algebraic systems of equations and accounts for more than 80 of the total CPU–time. Each nonlinear system requires at least the partial solution of a sequence of linear systems. We present a comparative study of iterative methods for solving these systems, where we apply both standard routines from the public domain package ITPACK 2C and our own routines tailored to the network problem. The conjugate gradient method, preconditioned by symmetric successive overrelaxation, was found to be consistently faster and more robust than the other solvers tested. In particular, it was found to be much superior to the successive overrelaxation technique currently used by many researchers.     

结构静态拓扑重分析的迭代组合近似方法

提出一种拓扑修改的静态重分析的迭代组合近似方法. 这种方法基本上是两步法. 首先，将新增加的自由度通过Guyan缩减方法凝聚到原始自由度上，形成凝聚方程. 其次， 用迭代组合近似方法求出原始自由度的近似位移，从而求出原结构自由度的位移. 新增加自 由度的位移可以通过恢复得到. 通过板结构的加筋布局优化设计的数值例子表明， 该方法对拓扑修改较大时仍可得到满意的结果.     

Investigation of the stability of a corona discharge continuum model in the shortwave approximation

The stability of a negative corona discharge between two spherical electrodes the inner of which is a hydrodynamic source is investigated. A continuum discharge model consisting of equations for the electrons and positive and negative ions written with allowance for electrokinetic reactions and electrodynamic equations is used. The steady-state (undisturbed) solution of this electrohydrodynamic system of equations is found using numerical methods and its stability is analyzed in the shortwave approximation for various structural zones of the corona discharge, namely, the ionization zone, the zone of attachment of electrons to neutral molecules, and the unipolar charge zone (negative ion zone). The perturbation growth rates in these zones are determined. It is shown that in the ionization zone the corona discharge considered is unstable.     

Approximate solution of a time-dependent differential equation

In this paper an asymptotic analytic solving method for a differential equation with complex function, small nonlinearity and a slow variable parameter is developed. The procedure is an extension of the well known Bogolubov-Mitropolski method. The correctness of the procedure is proved by an example. The vibrations of a rotor on which a thin band is wound and on which a small linear damping acts are obtained. The analytical solutions are compared with numerical ones. They are in good agreement.

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Sommario Nel presente lavoro viene sviluppato un metodo asintotico per la risoluzione analitica di equazioni differenziali di variabile complessa con piccola non-linearità e parametro lentamente variabile. La procedura proposta è un'estensione del ben noto metodo di Bogolubov-Mitropolski. La correttezza di tale procedura è provata su di un esempio. Sono ottenute le vibrazioni di un rotore su cui viene arrotolato uno strato sottile ed agisce un piccolo smorzamento lineare. Le soluzioni analitiche sono comparate con quelle numeriche con cui sono in buon accordo.

     

Numerical solution of a nonlinear reaction-diffusion equation

A nonlinear reaction-diffusion equation is studied numerically by a Petrov-Galerkinfinite element method,which has been proved to be2nd-order accurate in time and4th-orderin space.The comparison between the exact and numerical solutions of progressive wavesshows that this numerical scheme is quite accurate,stable and efficient.It is also shown thatany local disturbance will spread,have a full growth and finally form two progressive wavespropagating in both directions.The shape and the speed of the long term progressive wavesare determined by the system itself,and do not depend on the details of the initial values.