The finite difference migration, proposed and developed by J.F. Claerbout, is now widely used in seismic data processing. The method has a limitation that the events are not dipping too much. Guanquan ZHANG derived a new version of higher-order approximation of one-way wave equation in the form of systems of lower-order equations. For these systems he constructed some suitable difference schemes and developed a new algorithm of finite-difference migration for steep dips. In this paper, we discuss the stability of these difference schemes by the method of energy estimation.

The nearly linear triangular element approximation to the stationary Stokes problem has already been proposed. This paper discusses new rectangular and quadrilateral element approximations to the same problem, and the first order error is proved for both elements.

This paper is concerned with iterative procedures for the monotone complementarity problem. Our iterative methods consist of finding fixed points of appropriate continuous maps. In the case of the linear complementarity problem, it is shown that the problem is solvable if and only if the sequence of iterates is bounded in which case summability methods are used to find a solution of the problem. This procedure is then used to find a solution of the nonlinear complementarity problem satisfying certain regularity conditions for which the problem has a nonempty bounded solution set.

This paper discusses the sensitivity of semisimple multiple eigenvalues and corresponding invariant subspaces of a complex (or real) $n\times n$ matrix analytically dependent on several parameters. Some results of this paper may be useful for investigating robust multiple eigenvalue assignment in control system design.

This is the second half of the article. The rate of convergence for the $h$-$p$ version with geometric meshes is discussed.

In this paper, we consider the following problem $$\begin{cases}u''(x)=f(x,u(x),u'(x)), a\leq x\leq b,\\u(a)=u(b)=0,\end{cases}$$ and obtain the theorem.

Symplectic geometry plays a very important role in the research and development of Hamilton mechanics, which has been attracting increasing interest. Consequently, the study of the numerical methods with symplectic nature becomes a necessity.
Feng Kang introduced in [5] the concept of symplectic scheme of the Hamilton equation, and used the generating function methods to construct the symplectic scheme with arbitrarily precise order in the finite dimensional case, which can be applied to the ordinary differential equation, such as the two body problem. He also widened the traditional concept of generating function.
The authors in this paper use the method in the infinite dimensional case following [6], that is, using generating function methods to construct the difference scheme of arbitrary order of accuracy for partial differential equations which can be written as Hamilton system in the Banach space.  

A numerical method for coarse grids is proposed for the numerical solution of the incompressible Navier-Stokes equations. From singular perturbation considerations, we obtain partial differential equations and boundary conditions for the outer solution and the boundary layer correction. The former problem is solved with the finite difference method and the latter with the approximate method. Numerical experiments show that accurate outer flow and boundary flux result with little computational effort.