Numerical methods for transient behavior of semiconductor devices are studied.Mathematical model of a three-dimensional semiconductor device with heat conduction is described by a initial boundary value problem with four quasilinear partial differential equations.Finite difference fractional step method,characteristic finite element alternating direction method,domain decomposition method and theoretical analysis are focused on.

An efficient domain decomposition scheme for parabolic equations is discussed,which applies a modified upwind approximation to the first-order derivative.For parallel computation the scheme employs implicit procedures in subdomains and adopts explicit calculations with inter-domain boundaries.With a weaker stability constraint,error estimate in a discrete l² norm is presented.Theoretical analyses are validated by numerical experiments.

It outlines some mathematical problems in computational petroleum geology and puts forward the methods for solving them.

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.