Longjun Shen ¹, Guangwei Yuan ¹

In the present work we are going to solve the boundary value problem for the quasilinear parabolic systems of partial differential equations with two space dimensions by the finite difference method with intrinsic parallelism. Some fundamental behaviors of general finite difference schemes with intrinsic parallelism for the mentioned problems are studied. By the method of apriori estimation of the discrete solutions of the nonlinear difference systems, and the interpolation formulas of the various norms of the discrete functions and the fixedpoint technique in finite dimensional Euclidean apace, the existence of the discrete vector solutions of the nonlinear difference system with inreinsic parallelism are proved. Moreover the convergence of the discrete vector solutions of these difference schemes to th eunique generalized solution of the original quasilinear parabolic problem is proved.

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