论文标题
时间分数PDE的开放问题：需要存储所有数据
The open question of time fractional PDEs: needs to store all data
论文作者
论文摘要
众所周知，当前阶段的时间分数PDE的Nunerical解决方案取决于所有上述时间实例。因此，随着时间步长的增加，存储需求线性增长，这尤其是在高维问题的情况下构成了重大挑战。据我们所知，这仍然是时间分数PDE的一个悬而未决的问题。在本文中，我们提出了一种有效且无存储器的算法，以使用增量SVD来回答这个开放问题。数字体验表明，我们的新算法不仅没有内存，而且比标准求解器更有效。
It is well known that the nunerical solution of time fractional PDEs at current stage depends on all preceding time instances. Hence, the storage requirement grow linearly as the number of the time steps increases, which poses a significant challenge especially for high-dimensional problems. To the best of our knowledge, this is still an open question in the time fractional PDEs. In this paper, we propose an efficient and memory free algorithm to answer this open question by using incremental SVD. Numercial experiemnts show that our new algorithm not only memory free, but also more efficient than standard solvers.
