A family of Time-Accurate and highly-Stable Explicit (TASE) operators for the numerical solution of stiff IVPs that includes those proposed by Bassenne et al. (2021) [1] is proposed. In this family the TASE operator of order k depends on k free parameters in contrast with Bassenne's family in which it depends only on one parameter to be chosen for stability and accuracy requirements. A complete study of A–stability properties is carried out for explicit RK schemes supplemented with TASE operators with order $k\le 4$. For orders 2, 3 and 4, particular schemes that are nearly strongly A–stable and therefore suitable for stiff problems are given. Some numerical experiments showing the behaviour of the methods are presented.

一类时间精确且高度稳定的显式（TASE）运算符，用于刚性IVP的数值解，其中包括Bassenne等人提出的那些。（2021）提出了[1]。在该系列中，k阶的TASE运算符依赖于k个自由参数，而Bassenne族则仅依赖一个参数来选择其稳定性和准确性。对于显式RK方案，加上TASE运算符，对A稳定性性质进行了完整的研究$ķ\le 4$。对于2、3和4阶，给出了几乎是A稳定并且因此适用于刚性问题的特定方案。一些数值实验表明了该方法的行为。