Finite-difference schemes for time-dependent diffusion-convection problems (Q1569337)

The authors apply the general theory of stability of finite difference schemes for a model convection-diffusion problem in a rectangle. Symmetric control-difference approximations are used for the convective terms. Classical weighted schemes and splitting schemes of an alternating type are shown to be unconditionally stable. Schemes with explicit convective and implicit diffusion transfer are singled out as a separate class. The analysis is based on the general theory of stability of operator-difference schemes.