Du Fort-Frankel格式及DFF-I并行格式的稳定性

 本文对抛物型方程的Du Fort-Frankel(DFF)格式以及基于该格式构造的并行差分格式(DFF-I)进行了稳定性分析。采用矩阵分析方法, 证明了其无条件(LR)稳定性, 给出了DFF格式的稳定性系数的最小值的上界估计, 结果表明其与网格比有关, 从而DFF格式并非绝对稳定。本文改进了并行差分格式(DFF-I)的稳定性分析结果, 证明了其增长矩阵的谱半径严格小于1, 从而具有长时间稳定性。数值算例验证了DFF-I格式具有空间二阶精度, 且有很好的稳定性。

Stability of the du fort-frankel scheme and the parallel dff-i scheme

In this paper, we give the stability analysis on the Du Fort-Frankel(DFF) scheme and a parallel scheme (DFF-I) which is based on the DFF scheme and the fully implicit scheme. We analyze the DFF scheme by the matrix analysis method and the unconditional stability of the DFF scheme is proved. We obtain an explicit bound of the stability coefficients, which depend on the mesh ratio and show that the DFF scheme is not absolutely stable. For the DFF-I parallel scheme, we improve the stability results, and prove that the spectral radius of its growth matrix is less than 1. Numerical experiments show that the DFF-I parallel scheme has 2nd order accuracy in space and is stable.