Parallel difference schemes for parabolic problems

In this paper some implicit domain decomposition procedures for solving parabolic problems are proposed. In these methods, the classic implicit scheme is used in each sub-domain, and Dirichlet boundary values at the (interior) boundaries of sub-domains are just taken as the values of the difference solution at the previous time level. These implicit domain decomposition procedures are easy to be implemented on parallel computers and are called parallel difference schemes. They are proved to be stable and convergent unconditionally in discrete L/sup /spl infin// and H/sup 1/ norms, and the convergence order is O(/spl tau/ + h) though the truncation error at the sub-domain boundaries is O(1).