A high accurate alternating group 8-point scheme for convection diffusion problems is given. It can be used for parallel computing and is proved unconditionally stable. Numerical experiments show that the scheme has high accuracy.

Computer simulation for evolutionary history of an oil-gas bearing basin is to repeat its geological and thermodynamic evolutionary history on a computer. The mathematical model of basin simulation is characterised by an initial-boundary value problem of nonlinear partial differential equations on the abnormal pressure and the paleo-temperature of the formation. In the present paper, numerical method for three-dimensional proposed, the analysis on their stability and a numerical result for a practical model is given also. The results show that the abnormal pressure and the paleo-temperature computed are reasonable and display physical characteristics clearly as well.