A Strang-type alternating segment domain decomposition method for 2-D parabolic problems is proposed. The domain can be divided into non-overlapping multi-block sub-domains by the idea of alternating segments. Strang-type splitting technique reduces complexity of the solving of the high dimensional problems by a series of one-dimensional ones. The method is proved to be unconditionally stable and truncation error is analyzed. Numerical experiments show that convergence rates in time and space are both second order.

A high accurate alternating group 8-point scheme for convection diffusion problems is given. It can be used for parallel computing and is proved unconditionally stable. Numerical experiments show that the scheme has high accuracy.