Unconditionally stable schemes for convection-diffusion problems

Convection-diffusion problems are basic ones in continuum mechanics. The main features of these problems are connected with the fact that their operators may have an indefinite sign. In this paper we study the stability of difference schemes with weights for convection-diffusion problems where the convective transport operator may have various forms. We construct unconditionally stable schemes for nonstationary convection-diffusion equations based on the use of new variables. Similar schemes are also used for parabolic equations where the operator represents the sum of diffusion operators.