Parabolic Equation For A Class Of Alternating Group Iterative Method

Two kind of new parallel iterative algorithm for solving Crank-Nicolson difference scheme of parabolic equation is constructed in this paper. The basic idea is to divide the system of implicit difference equations into a set of subsystem that can be solved individually in parallel. The process of constructing the algorithm is given. The property of convergence is proved by matrix theory. The results of numerical experiment of some examples are obtained. It shows that the analysis of theory is correct and the algorithm is feasible and efficient.In the end of the paper, we point out problems unsolved and indicate direction of research in the future.