The momentary state of a semiconductor device is described with three nonlinear partial differential equations. A finite difference scheme for transient behaviors of two-dimensional semiconductor devices on grids with local refinement in time and space is constructed and studied.The electrostatic potential equation is approximated by a five-point difference scheme.The electron and the hole density equations are discretized by a modified upwind scheme.The construction uses a linear interpolation at slave nodes.An error analysis is presented and illustrated with a numerical example.

Parallel numerical simulation of migration-accumulation of oil resources in porous media is to describe the process of oil migration and accumulation in basin evolution.It is of great value to the evaluation of oil resources and to the determination of the location and amount of oil deposite.This paper puts forward a numerical model,a parallel operator splitting-up implicit iterative scheme,parallel arithmetic program,parallel arithmetic information and alternating-direction mesh subdivision.It also discusses computation and analysis of different mesh step lengths.For the actual situation of Tanhai region of Shengli Petroleum Field,the numerical simulation test results and the actual conditions are coincident.For the model problem (nonlinear coupled system) optimal order estimates in l² norm are derived to determine the errors.The problem in the fields of permeation fluid mechanics and petroleus geology appears to be solved.

Numerical simulation in oil-field exploration and exploitation with computational mathematics and dynamics of fluids in porous media is discussed. The numerical method of nuclear waste disposal contamination, prediction and prevention of sea-water intrusion and the numerical simulation of transient behavior of semi-conductor devices are also studied. The mathematical model is the nonlinear convection-dominated diffusion coupled systems with initial-boundary value problem. Characteristic finite difference method, characteristic finite element method, fractional step numerical method and its theoretical analysis are mainly dealed with.

The simulation of the process and the effects of protection projects lays the foundation of its effective control and defence. A mathematical model of the problem and the upwind fractional step finite difference method are presented. Using this method, the numerical simulation of seawater intrusion in Laizhou Bay Area of Shandong Province is given. The numerical results turn out to be identical with the real measurements, so the prediction of the consequences of protection projects is reasonable.

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.