A HIGH ORDER DIFFERENCE METHOD FOR FRACTIONAL SUB-DIFFUSION EQUATIONS WITH THE SPATIALLY VARIABLE COEFFICIENTS UNDER PERIODIC BOUNDARY CONDITIONS

Huiqin Zhang; Yan Mo; Zhibo Wang

doi:10.11948/20180150

2020 Volume 10 Issue 2

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Huiqin Zhang, Yan Mo, Zhibo Wang. A HIGH ORDER DIFFERENCE METHOD FOR FRACTIONAL SUB-DIFFUSION EQUATIONS WITH THE SPATIALLY VARIABLE COEFFICIENTS UNDER PERIODIC BOUNDARY CONDITIONS[J]. Journal of Applied Analysis & Computation, 2020, 10(2): 474-485. doi: 10.11948/20180150

Citation:

Huiqin Zhang, Yan Mo, Zhibo Wang. A HIGH ORDER DIFFERENCE METHOD FOR FRACTIONAL SUB-DIFFUSION EQUATIONS WITH THE SPATIALLY VARIABLE COEFFICIENTS UNDER PERIODIC BOUNDARY CONDITIONS[J]. Journal of Applied Analysis & Computation, 2020, 10(2): 474-485. doi: 10.11948/20180150

A HIGH ORDER DIFFERENCE METHOD FOR FRACTIONAL SUB-DIFFUSION EQUATIONS WITH THE SPATIALLY VARIABLE COEFFICIENTS UNDER PERIODIC BOUNDARY CONDITIONS

1.
School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510006, Guangdong, China

Corresponding author: Email address: wzbmath@gdut.edu.cn(Z. Wang)
Fund Project: This research is supported by the National Natural Science Foundation of China (No. 11701103, 11801095), Natural Science Foundation of Guangdong Province (No. 2017A030310538, 2019A1515010876), the Project of Science and Technology of Guangzhou (No. 201904010341), Young Top-notch Talent Program of Guangdong Province (No. 2017GC010379), the Project of Department of Education of Guangdong Province (No. 2017KTSCX062) and the grant from Guangdong University of Technology (Nos. 220413131 & No. 220413550)

Abstract

Abstract

In this paper, we propose a difference scheme with global convergence order O(τ² + h⁴) for a class of the Caputo fractional equation. The difficulty caused by the spatially variable coefficients is successfully handled. The unique solvability, stability and convergence of the finite difference scheme are proved by use of the Fourier method. The obtained theoretical results are supported by numerical experiments.
- Fractional diffusion equation /
- Fourier method /
- variable coefficients /
- stability /
- convergence
MSC: 65M06, 65M12, 65M15, 35R11

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References

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