• Abstract

For the large sparse systems of linear and nonlinear equations, a new class of generalized asynchronous parallel multisplitting iterative method is presented, and its convergence theory is established under suitable conditions. This method not only unifies the discussions of various existing asynchronous multisplitting iterations, but also affords new algorithmic and theoretical results for the parallel solution of large sparse system of linear equations.Besides its generality, this method is also much more suitable for implementing on the MIMD multiprocessor systems.

• Abstract

In the theoretical study of numerical solution of stiff ODEs, it usually assumes that the righthand function f(y) satisfy one-side Lipschitz condition < f(y)-f(z),y-z >= v' ||y-z||_2,f:Omega C m to C~m, or another related one-side Lipschitz condition [F(Y)-F(Z),Y-Z]_D <= v" ||Y-Z||~2_D,F:Omega~S C~(ms) to C~(ms), this paper demonstrates that the difference of the two sets of all functions satisfying the above two conditions respectively is at most that v'-v" only is constant independent of stiffness of function f.

• Abstract

In this paper,the phenomena of spirals are numerically presented by MmB scheme for initial value problems of 2-D gas dynamics (y=1.4), which include 2-D Riemann problems and continuous initial value problems.In isentropic flow, for high speed rotation (v_0/c_0 < KF 2 KF), there is a region of vacuum at the origin and for low speed rotation (v_0/c_0 < KF 2 KF), there is no vacuum, and for adiabatic flow, the structure of spirals is also discussed.

• Abstract

• Abstract

A combined Legenedre spectral-finite element approximation is proposed for solving two-dimensional unsteady Navier-Stokes equation. The artificial compressibility is used. The generalized stability and convergence are proved strictly. Some numerical results show the advantages of this method.

• Abstract

In this paper, we construct the real-valued periodic orthogonal wavelets. The method presented here is new. The decomposition and reconstruction formulas involve only 4 terms respectively. It demonstrates that the formulas are simpler than that in other kinds of periodic wavelets. Our wavelets are useful in applications since it is real valued. The relation between the periodic wavelets and the Fourier series is also discussed.

• Abstract

This paper deals with the asymptotic stability of theoretical solutions and numerical methods for the delay differential equations (DDEs):y'(t) =ay(t) + Sum DD(m, j = 1 .. b_jy(lambda_jt) t >= y_0, where a, b_1, b_2, ... b_m and y_0 \in C, 0 > lambda_m \le \lambda_m-1 \le ... \le \lambda_1). A sufficient condition such that the differential equations are asymptotically stable is derived. And it is shown that the linear theta-method is OmegaGP_m-stable if and only if SX 1 2 SX \le theta \le 1.

• Abstract

In this paper, an optimal V-cycle multigrid algorithm for some famous nonconforming plate elements is established.

• Abstract

This paper,based on the general forms of the penalties by Beale and Small and the stronger penalties by Tomlin, describes the modifications of these penalties used for the method of bounded variables. The same examples from Petersen are taken and the satisfactory results are shown in comparison with those obtained by Tomlin.

• Abstract

This paper studies the geometric structure of nonlinear Schrodinger equation and from the view-point of preserving structure a kind of fully discrete schemes is presented for the numerical simulation of this important equation in quantum. It has been shown by theoretical anaysis and numerical experiments that such discrete schemes are quite satisfactory in keeping the desirable conservation properties and for simulating the long-time behaviour.