Difference schemes with intrinsic parallelism for quasi-linear parabolic systems

The boundary value problem for quasi-linear parabolic system is solved by the finite difference method with intrinsic parallelism. The existence and uniqueness and convergence theorems of the discrete vector solutions of the nonlinear difference system with intrinsic parallelism are proved. The limiting vector function is just the unique generalized solution of the original problem for the parabolic system. Project supported by the National Natural Science Foundation of China and the Foundation of Chinese Academy of Engineering Physics.