In this paper, the linear finite element approximation to the elastic contact problem with curved contact boundary is considered. The error bound $O(h^{1/2})$ is obtained with requirements of two times continuously differentiable for contact boundary and the usual regular triangulation, while I.Hlavacek et. al. obtained the error bound $O(h^{3/4})$ with requirements of three times continuously differentiable for contact boundary and extra regularities of triangulation (c.f. [2]).  

In this paper we propose the two kinds of different criteria and use them to judge the convergence of Durand-Kerner method and to compare the obtained results with other methods.

Semidiscretization in space of nonlinear degenerate parabolic equations of nondivergent form is presented, under zero Dirichlet boundary condition. It is shown that semidiscrete solutions blow up in finite time. In particular, the asymptotic behavior of blowing-up solutions, is discussed precisely.

In this paper, we propose two new perturbation simplex variants. Solving linear programming problems without introducing artificial variables, each of the two uses the dual pivot rule to achieve primal feasibility, and then the primal pivot rule to achieve optimality. The second algorithm, a modification of the first, is designed to handle highly degenerate problems more efficiently. Some interesting results concerning merit of the perturbation are established. Numerical results from preliminary tests are also reported.  

$A = (a_{ij}) \in R^{n×n}$ is termed bisymmetric matrix if $$a_{ij} = a_{ji} = a_{n-j+1,n-i+1}, i,j=1,2, ..., n.$$ We denote the set of all $n \times n$ bisymmetric matrices by $BSR^{n×n}$.
This paper is mainly concerned with solving the following two problems:
Problem I. Given $X, B \in R^{n×m}$, find $A \in P_n$ such that $AX=B$, where $P_n = \{ A \in BSR^{n×n}| x^TAx \ge 0, \forall x \in R^n \}$.
Problem Ⅱ. Given $A^* \in R^{n×n}$, find $\hat{A} \in S_E$ such that $$\| A^* -\hat{A}\|_F =\mathop{min}\limits_{A \in S_E} \| A^* - A \|_F,$$ where $\|\cdot\|_F$ is Frobenius norm, and $S_E$ denotes the solution set of problem I.

The necessary and sufficient conditions for the solvability of problem I have been studied. The general form of $S_E$ has been given. For problem II the expression of the solution has been provided.

This paper describes practical approaches on how to construct bounding pyramids and bounding cones for triangular Bézier surfaces. Examples are provided to illustrate the process of construction and comparison is made between various surface bounding volumes. Furthermore, as a starting point for the construction, we provide a way to compute hodographs of triangular Bézier surfaces and improve the algorithm for computing the bounding cone of a set of vectors.  

In this paper we present two algorithms for $LC^1$ unconstrained optimization problems which use the second order Dini upper directional derivative. These methods are simple and easy to perform. We discuss the related properties of the iteration function, and establish the global and superlinear convergence of our methods.  

The main purpose of the present paper is to examine the existence and local uniqueness of solutions of the implicit equations arising in the application of a weakly algebraically stable general linear methods to dissipative dynamical systems, and to extend the existing relevant results of Runge-Kutta methods by Humphries and Stuart (1994).  

A discontinuous finite element method for convection-diffusion equations is proposed and analyzed. This scheme is designed to produce an approximate solution which is completely discontinuous. Optimal order of convergence is obtained for model problem. This is the same convergence rate known for the classical methods.

The main results of this paper are as follows: (1) Suppose an s stage Runge-Kutta method is consistent, irreducible, non-confluent and symplectic. Then this method is of order at least $2p+l(1 \le p \le s-1)$ provided that the simplifying conditions $C(p)$ (or $D(p)$ with non-zero weights) and $B(2p+l)$ hold, where $l=0,1,2.$ (2) Suppose an s stage Runge-Kutta method is consistent, irreducible and non-confluent, and satisfies the simplifying conditions $C(p)$ and $D(p)$ with $0 ＜ p \le s.$ Then this method is symplectic if and only if either $p = s$ or the nonlinear stablility matrix $M$ of the method has an $(s-p)×(s-p)$ chief submatrix $\hat{M}=0.$ (3) Using the results (1) and (2) as bases, we present a general approach for the construction of symplectic Runge-Kutta methods, and a software has benn designed, by means of which, the coefficients of s stage symplectic Runge-Kutta methods satisfying $C(p), D(p)$ and $B(2p+l)$ can be easily computed, where $1 \le p \le s, 0 \le l \le 2, s \le 2p+l \le 2s.$  

There are two cases of the exterior problems of the Helmholtz equation. If λ≥0 the bilinear form is coercive, and if λ＜0 it is the scattering problem. We give a new approach of the infinite element method, which enables us to solve these exterior problems as well as corner problems. A numerical example of the scattering problem is given.