In this paper, we will prove by the help of formal energies only that one can improve the order of any symplectic scheme by modifying the Hamiltonian symbol $H$, and show through examples that this action exactly and directly simplifies Feng's way of construction of higher-order symplectic schemes by using higher-order terms of generating functions.

In this paper, the asymptotic error expansions of Adini's element for the second order inhomogeneous Neumann problem are given and the superconvergence estimations are obtained. Moreover, a numerical example to support our theoretical analysis is reported.

A class of asynchronous nested matrix multisplitting methods for solving large-scale systems of linear equations are proposed, and their convergence characterizations are studied in detail when the coefficient matrices of the linear systems are monotone matrices and $H$-matrices, respectively.

Least squares solution of F=PG with respect to positive semidefinite symmetric P is considered, a new necessary and sufficient condition for solvability is given, and the expression of solution is derived in the some special cases. Based on the expression, the least squares solution of an inverse eigenvalue problem for positive semidefinite symmetric matrices is also given.

In this paper we represent a new numerical method for solving the steady Navier-Stokes equations in three dimensional unbounded domain. The method consists in coupling the boundary integral and the finite element nonlinear Galerkin methods. An artificial smooth boundary is introduced separating an interior inhomogeneous region from an exterior one. The Navier-Stokes equations in the exterior region are approximated by the Oseen equations and the approximate solution is represented by an integral equation over the artificial boundary. Moreover, a finite element nonlinear Galerkin method is used to approximate the resulting variational problem. Finally, the existence and error estimates are derived.

The convergences ununiformly and uniformly are established for the nonconforming finite element methods for the second order elliptic problem with the lowest regularity, i.e., in the case that the solution $u \in H^1_0(\Omega)$ only.

In this paper, following our original ideas, we first consider a weakly overlapping additive Schwarz preconditioner according to the framework of [2] for Morley element and show that its condition number is quasi-optimal; we then analyze in detail the structure of this preconditioner, and after proper choices of the inexact solvers, we obtain a quasi-optimal nonoverlapping domain decomposition preconditioner in the last. Compared with [12], [13], it seems that according to this paper's procedure we can make out more thoroughly the relationship between overlapping and nonoverlapping domain decomposition methods for nonconforming plate elements, and certainly, we have also proposed another formal and simple strategy to construct nonoverlapping domain decomposition preconditioners for nonconforming plate elements.

Many authors have studied the Rayleigh quotient and Rayleigh quotient matrix. This paper consists of two parts. First, generalizations of some results on the Rayleigh quotient are proved. Second, we give some applications of these theoretical results.

It is well known that mono-implicit Runge-Kutta methods have been applied in the efficient numerical solution of initial or boundary value problems of ordinary differential equations. Burrage(1994) has shown that the order of an s-stage mono-implicit Runge-Kutta method is at most s+1 and the stage order is at most 3. In this paper, it is shown that the order of an s-stage mono-implicit Runge-Kutta method being algebraically stable is at most min $(\widetilde{s}, 4)$, and the stage order together with the optimal B-convergence order is at most min(s,2), where 

The line search strategy is crucial for an efficient unconstrained optimization algorithm. One of the reason why the Wolfe line searches is recommended lies in that it ensures positive definiteness of BFGS updates. When gradient information has to be obtained costly, the Armijo-Goldstein line searches may be preferred. To maintain positive definiteness of BFGS updates based on the Armijo-Goldstein line searches, a slightly modified form of BFGS update is proposed by I.D. Coope and C.J. Price (Journal of Computational Mathematics, 13 (1995), 156-160), while its convergence properties is open up to now. This paper shows that the modified BFGS algorithm is globally and superlinearly convergent based on the Armijo-Goldstein line searches.

This paper considers the generalized difference methods on arbitrary networks for Poisson equations. Convergence order estimates are proved based on some a priori estimates. A supporting numerical example is provided.