Several effective algorithms for nonlinear time fractional models

摘要

In this paper, several effective algorithms are proposed to simulate the time fractional models. A complete analysis of the algorithms for nonlinear problems is presented, while the previous investigations mainly focus on construction and analysis of L1-type method for the linear time fractional problems. After that, by using the sum-of-exponentials approximation, we develop the corresponding accelerated methods. We obtain that computational cost is reduced from O(N2) to O(logN) or O(log2N), where N denotes total number of time steps. Finally, several numerical experiments on several real-world models are proposed to confirm the effectiveness of the algorithms.