A note on second-order finite-difference schemes on uniform meshes for advection-diffusion equations

An artificial-viscosity finite-difference scheme is introduced for stabiliz ing the solutions of advection-diffusion equations. Although only the linea r one-dimensional case is discussed, the method is easily susceptible to ge neralization. Some theory and comparisons with other well-known schemes are carried out. The aim is, however, to explain the construction of the metho d, rather than considering sophisticated applications. (C) 1999 John Wiley & Sons, Inc.