We construct efficient implicit-explicit BDF$k$ scalar auxiliary variable (SAV) schemes for general dissipative systems. We show that these schemes are unconditionally stable, and lead to a uniform bound of the numerical solution in the norm based on the principal linear operator in the energy. Based on this uniform bound, we carry out a rigorous error analysis for the $k$th-order $(k=1,2,3,4,5)$ SAV schemes in a unified form for a class of typical Allen-Cahn type and Cahn-Hilliard type equations. We also present numerical results confirming our theoretical convergence rates.

翻译：我们为一般消散系统设计了高效的隐性BDF$kk元卡路里辅助变量(SAV)计划,我们证明这些计划是无条件稳定的,导致基于能源主要线性运营商的规范中数字解决方案的统一约束,根据这一统一约束,我们对典型的Allen-Cahn型和Cahn-Hilliard型方程式的统一形式,对美元(k=1,2,3,4,5美元)的SAV计划进行了严格的错误分析,并提供了证实我们理论趋同率的数字结果。