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

BDF$6$ SAV schemes for time-fractional Allen-Cahn dissipative systems