We consider a time-fractional subdiffusion equation with a Caputo derivative in time, a general second-order elliptic spatial operator, and a right-hand side that is non-smooth in time. The presence of the latter may lead to locking problems in our time stepping procedure recently introduced in [2,4]. Hence, a generalized version of the residual barrier is proposed to rectify the issue. We also consider related alternatives to this generalized algorithm, and, furthermore, show that this new residual barrier may be useful in the case of a negative reaction coefficient.

翻译：考虑时间分数阶次扩散方程，方程中包含时间Caputo导数、一般二阶椭圆空间算子以及时间上非光滑的右端项。这类右端项的存在可能导致文献[2,4]中最近提出的时间步长过程出现锁定问题。为此，我们提出残差屏障的广义化版本来修正该问题。同时探讨该广义算法的相关替代方案，并进一步证明这种新型残差屏障在负反应系数情形下同样具有适用性。