TY - JOUR
T1 - Fast Evaluation of the Caputo Fractional Derivative and Its Applications to Fractional Diffusion Equations: A Second-Order Scheme
AU - Yonggui Yan, Zhi-Zhong Sun & Jiwei Zhang
JO - Communications in Computational Physics
VL - 4
SP - 1028
EP - 1048
PY - 2017
DA - 2017/10
SN - 22
DO - http://doi.org/10.4208/cicp.OA-2017-0019
UR - https://global-sci.org/intro/article_detail/cicp/9992.html
KW - 
AB - <p style="text-align: justify;">The fractional derivatives include nonlocal information and thus their calculation
requires huge storage and computational cost for long time simulations. We
present an efficient and high-order accurate numerical formula to speed up the evaluation
of the Caputo fractional derivative based on the L2-1<sub>σ</sub> formula proposed in
[A. Alikhanov, J. Comput. Phys., 280 (2015), pp. 424-438], and employing the sum-of-exponentials
approximation to the kernel function appeared in the Caputo fractional
derivative. Both theoretically and numerically, we prove that while applied to solving
time fractional diffusion equations, our scheme not only has unconditional stability
and high accuracy but also reduces the storage and computational cost.</p>