Guangwei Yuan ¹, Longjun Shen ¹

In this paper we are going to discuss the difference schemes with intrinsic parallelism for the boundary value problem of the two dimensional semilinear parabolic systems. The unconditional stability of the general finite difference schemes with intrinsic parallelism is justified in the sense of the continuous dependence of the discrete vector solution of the difference schemes on the discrete data of the original problems in the discrete $W^{(1,2)}_2$ norms. Then the uniqueness of the discrete vector solution of this difference scheme follows as the consequence of the stability.

Key words: Difference Scheme; Intrinsic Parallelism; Two Dimensional Semilinear Parabolic System; Stability.