New asymmetric difference schemes for dispersive equations with diffusion are given. A parallel alternating segment difference scheme for solving the equation is constructed, which is unconditionally stable, and can be used directly on parallel computers. Numerical experiments for the model problem are performed, and the results are reported.

A class of alternating group method of four points for solving diffusion equation is presented here. The method is unconditionally stable and has the obvious property of parallelism. This method can be used directly on parallel computers. Numerical experiments show that the method has high accuracy.

A kind of alternating segment Crank Nicolson method for solving Burgers equation is presented. The method is uncoditionally stable by analysis of linearization procedure and has the intrinsic parallelism with high accuracy.

To infuse water into oil reserrvoir by high-pressure pump,then the oil residua flow out of oil well,this is a problem of two-phase immiscible flow displacement,where are an important means of the modern oil extracting process. The mathematical model of the problem is the initial boundary problem of systems of partial differential equation.We have set up some computational scheme by the numerical method of differential discrete operator,also we have studied approximute and convergence theorem of continuous-time approximation and discrete-time approximations. At last, we have computed the two-dimensional problem by using the numerical method,the computation result is rational and shows the stability of the methods.