A parallel in time/spectral collocation combined with finite difference method for the time fractional differential equations

被引：5
作者：
Li X. [1 ]
Su Y. [1 ]
机构：
[1] Department of Mathematics and Computer Science, Fuzhou University, Fuzhou
来源：
Journal of Algorithms and Computational Technology | 2021年 / 15卷
基金：
美国国家科学基金会; 中国国家自然科学基金;
关键词：
finite difference method; spectral collocation method; time fractional differential equations; Time parareal;
D O I：
10.1177/17483026211008409
中图分类号：
学科分类号：
摘要：
In this article, we consider the numerical solution for the time fractional differential equations (TFDEs). We propose a parallel in time method, combined with a spectral collocation scheme and the finite difference scheme for the TFDEs. The parallel in time method follows the same sprit as the domain decomposition that consists in breaking the domain of computation into subdomains and solving iteratively the sub-problems over each subdomain in a parallel way. Concretely, the iterative scheme falls in the category of the predictor-corrector scheme, where the predictor is solved by finite difference method in a sequential way, while the corrector is solved by computing the difference between spectral collocation and finite difference method in a parallel way. The solution of the iterative method converges to the solution of the spectral method with high accuracy. Some numerical tests are performed to confirm the efficiency of the method in three areas: (i) convergence behaviors with respect to the discretization parameters are tested; (ii) the overall CPU time in parallel machine is compared with that for solving the original problem by spectral method in a single processor; (iii) for the fixed precision, while the parallel elements grow larger, the iteration number of the parallel method always keep constant, which plays the key role in the efficiency of the time parallel method. © The Author(s) 2021.
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