@Article{NMTMA-13-433,
author = {Gao , Guanghua and Yang , Qian},
title = {Fast Evaluation of Linear Combinations of Caputo Fractional Derivatives and Its Applications to Multi-Term Time-Fractional Sub-Diffusion Equations},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2020},
volume = {13},
number = {2},
pages = {433--451},
abstract = {<p style="text-align: justify;">In the present work, linear combinations of Caputo fractional derivatives are fast evaluated based on the efficient sum-of-exponentials (SOE) approximation for&nbsp; kernels in Caputo fractional derivatives with an absolute error $\epsilon,$&nbsp; which is a further work of the existing results in [13]&nbsp; (Commun. Comput. Phys., 21 (2017), pp. 650-678) and [16] (Commun. Comput. Phys., 22 (2017), pp. 1028-1048). Both the storage needs and computational amount are&nbsp; significantly reduced compared with the direct algorithm. Applications of the proposed fast algorithm are illustrated by solving a second-order multi-term time-fractional sub-diffusion problem. The unconditional stability and convergence of the fast difference scheme are proved. The CPU time is largely reduced while the accuracy is kept, especially for the cases of&nbsp; large&nbsp; temporal level, which is displayed by&nbsp; numerical experiments.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2019-0013},
url = {http://global-sci.org/intro/article_detail/nmtma/15486.html}
}