Recently, the error analysis of BDF$k$ $(1\leqslant k\leqslant5)$ SAV (scalar auxiliary variable) schemes are given in \cite{Huangg:20} for the classical Allen-Cahn equation. However, it remains unavailable for BDF$6$ SAV schemes. In this paper, we construct and analyze BDF$6$ SAV schemes for the time-fractional dissipative systems. We carry out a rigorous error analysis for the time-fractional Allen-Cahn equation, which also fills up a gap for the classical case. Finally, numerical experiment is shown to illustrate the effectiveness of the presented methods. As far as we know, this is the first SAV schemes for the time-fractional dissipative systems.

翻译：最近,对古典Allen-Cahn等式的SAV(1\leqslant k\leqslant k\leqslant5)$SAV(calar 辅助变量)方案的错误分析在\ cite{Hwanng:20}中给出,但是,对于BDF$6$SAV计划,它仍然无法进行。在本文中,我们为时间偏差的消散系统建造和分析了6BDF$SAV计划。我们对时间偏差的Allen-Cahn等式进行了严格的错误分析,这也填补了古典案例的空白。最后,数字实验显示了所提出的方法的有效性。据我们所知,这是对时间偏差的系统的第一个SAV计划。