Characteristic Finite Difference Methods for Moving Boundary Value Problem of Numerical Simulation of Oil Deposit

<正> The software for oil-gas transport and accumulation is to describe the history of oil-gas transport and accumulation in basin evolution. It is of great value in rational evaluation of prospecting and exploiting oil-gas resources. The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary value problem. This paper puts forward a kind of characteristic finite difference schemes, and derives from them optimal order estimates in l2 norm for the error in the approximate solutions. The research is important both theoretically and practically for the model analysis in the field, for model numerical method and for software development.