Numerical method for solving the fractional evolutionary model of bi-flux diffusion processes

Abstract

In this paper, based on the nonuniform time meshes, we proposed an efficient difference scheme for solving the time-fractional bi-flux diffusion equation. By the energy method, we then proved that the present scheme is unconditionally stable and convergent in $L^2$ norm. Several numerical examples are given to verify the theoretical results. In addition, numerical simulations show the order of fractional derivative affects the diffusion rate of the particles.

Keywords:

• Bi-flux diffusion
• fractional evolutionary model
• numerical scheme
• stability
• error analysis

2010 AMS SUBJECT CLASSIFICATIONS:

• 35G16
• 65M06
• 65M12

Acknowledgments

The authors are deeply grateful to the anonymous reviewers for their valuable comments and suggestions which greatly enhance the quality of this manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Cui-cui Ji was partially supported by National Natural Science Foundation of China [grant number 12001307] and Natural Science Foundation of Shandong Province [grant numbers ZR2020QA033, ZR2021MA072]. Maosheng Jiang was partially supported by National Natural Science Foundation of China [grant number 12071046], Natural Science Foundation of Shandong Province [grant number ZR2021QA018] and China Postdoctoral Science Foundation [grant number 2022M721757].