The open question of time fractional PDEs: needs to store all data

Abstract: 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.