Author(s)

Xiaoxue Lu¹, Chunhua Zhang¹, Huiling Xue², Bowen Zhong^3*

¹College of Mathematics and Information Science, Nanchang Hangkong University, Nanchang, China.
²School of Statistics and Data Science, Jiangxi University of Finance and Economics, Nanchang, China.
³School of Aircraft Engineering, Nanchang Hangkong University, Nanchang, China.

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.

Variable-Order Caputo Fractional Derivative, Combined Compact Difference Method, Exponential-Sum-Approximation

Lu, X. , Zhang, C. , Xue, H. and Zhong, B. (2024) A Hybrid ESA-CCD Method for Variable-Order Time-Fractional Diffusion Equations. Journal of Applied Mathematics and Physics, 12, 3053-3065. doi: 10.4236/jamp.2024.129183.