Unconditional stability of parallel alternating difference schemes for semilinear parabolic systems

The general alternating schemes with intrinsic parallelism for semilinear parabolic systems are studied. First we prove the a priori estimates in the discrete H-1 space of the difference solution for these schemes. Then the existence of the difference solution for these schemes follows from the fixed point principle. Finally the unconditional stability of the general alternating schemes is proved. The alternating group explicit scheme, the alternating segment explicit-implicit scheme and the alternating segment Crank-Nicolson scheme are the special cases of the general alternating schemes. (C) 2001 Elsevier Science Inc. All rights reserved.