It presents the AGE(Alternating Group Explicit) method for solving the two-dimensional Burgers equation.The method is unconditionally stable by analysis of linearization procedure and has obvious property of parallelism.Numerical example is given at the shared memory computer.

The Block ADI(Alternating Direction Implicit) method for solving the two-dimensional convection diffusion equation is developed in this paper.The Block ADI method is unconditionally stable and has the localization property of both computation and communication,so the method can be used on the massively parallel processing system with distributed memory processors.The numerical example is given on a parallel system of networks of work stations.

A class GE (group explicit) methods for the convection equation based on explicit or implicit upwind schemes are presented. Consistency and (weakly) stability of numerical solutions are proved. Some numerical results illustrating the methods are given.

A new group explicit scheme for solving Burgers equation is constructed by the conservative Samarskii scheme. The linear stability of this method is discussed. Some numerical examples are given which illustrated that the present method is more suitable than Evans's method for solving Burgers equation with a large Reynolds number.

We consider the problem of constructing artificial boundary conditions for the wave equation. Two new boundary conditions are presented directly by a difference approximation. The stability of these boundary conditions and their consistency with the analytical boundary conditions are proved. Numericl examples indicate that these boundary conditions work effectively.

With the varieties of the cell Reynolds number,We analyse the properties of the upwind scheme, the Samarskii Scheme and the modified Dennis scheme for convection-diffusion equations. Three semi-implicit schemes which are unconditionally stable and monotonic are present by those schemes. Numerical tests have shown these semi-implicit can be applied to solve for the steady fluid flow problems of high Reynolds.