Scalar auxiliary variable (SAV) methods are a class of linear schemes for solving gradient flows that are known for the stability of a `modified' energy. In this paper, we propose an improved SAV (iSAV) scheme that not only retains the complete linearity but also ensures rigorously the stability of the original energy. The convergence and optimal error bound are rigorously established for the iSAV scheme and discussions are made for its high-order extension. Extensive numerical experiments are done to validate the convergence, robustness and energy stability of iSAV, and some comparisons are made.

翻译：标量辅助变量（SAV）方法是一类用于求解梯度流的线性格式，以其对‘修正’能量的稳定性而著称。本文提出了一种改进的SAV（iSAV）格式，该格式不仅保留了完全线性特性，还严格确保了原始能量的稳定性。针对iSAV格式，我们严格建立了收敛性和最优误差界，并讨论了其高阶扩展形式。通过大量数值实验验证了iSAV的收敛性、鲁棒性和能量稳定性，并进行了相关比较分析。