TITLE:
A Hybrid ESA-CCD Method for Variable-Order Time-Fractional Diffusion Equations
AUTHORS:
Xiaoxue Lu, Chunhua Zhang, Huiling Xue, Bowen Zhong
KEYWORDS:
Variable-Order Caputo Fractional Derivative, Combined Compact Difference Method, Exponential-Sum-Approximation
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.12 No.9,
September
10,
2024
ABSTRACT: In this paper, we study the solutions for variable-order time-fractional diffusion equations. A three-point combined compact difference (CCD) method is used to discretize the spatial variables to achieve sixth-order accuracy, while the exponential-sum-approximation (ESA) is used to approximate the variable-order Caputo fractional derivative in the temporal direction, and a novel spatial sixth-order hybrid ESA-CCD method is implemented successfully. Finally, the accuracy of the proposed method is verified by numerical experiments.