High order compact schemes for unsteady diffusion-convection problems I

For unsteady 2D diffusion-convection problems, we present Two classes of co mpact difference schemes of oi-der 2 in time and 4 in space. These FDS are essentially derived from 1D schemes, extensively analyzed in our previous p aper [6]. We propose two approaches: construction of 2D schemes as product of 1D schemes and global formulation of 2D schemes. Part II (by Michel Four nie) focuses on the development and analysis of global schemes with the ass istance of symbolic computation software (AXIOM). (C) Academie des Sciences /Elsevier, Paris.