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The difference method with intrinsic parallelism for two dimensional parabolic system is studied. The general alternating difference schemes, in particular those with variable time steplengthes, are constructed and proved to be unconditionally stable. The two dimensional alternating group explicit scheme, alternating block explicit-implicit scheme, alternating block Crank-Nicolson scheme and block ADI scheme are the special cases of the general schemes constructed here.

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Two classes of relaxed parallel two-stage multisplitting methods based on extrapolated and AOR methods are studied for the solution of nonsingular linear systems, which are called outer relaxed or inner relaxed parallel two-stage multisplitting methods. Convergence of these methods is studied for H-matrix. Furthermore, computational results about these methods on a shared memory multiprocessor are presented. The results show that the methods we proposed are better than the corresponding existed parallel (two-stage) multisplitting methods.