Unconditional stability of alternating difference schemes with intrinsic parallelism for two-dimensional fourth-order diffusion equation

Abstract

In this paper, the parallel difference schemes for parabolic equation are studied. The general alternating difference schemes with intrinsic parallelism for two-dimensional fourth-order diffusion equation are presented and proved to be unconditionally stable by the energy method. Two kinds of alternating band explicit (ABE1, ABE2) schemes, alternating band explicit–implicit (ABE–I) scheme and alternating band Crank–Nicolson (ABC–N) scheme are the special cases of the general schemes constructed here. Numerical experiments are performed to examine the accuracy and unconditional stability.