An alternating segment Crank-Nicholson method for the diffusion equation is constructed.The method is unconditionally stable and has the obvious property of parallelism.Numerical results for an example show this new method has satisfactory.

The parallel algorithms for solving the implicit difference equations have been studied in the paper. The basic idea is to divide the system of difference equations into a set of subsystems which can be solved in parallel. The direct method and iterative method are given and the convergence theorem on the iteration is proved. To show the efficiency of the segment implicit iteration, the papper gives the numerical experiment for an example of the diffusion equation.