A NEW ITERATION ALGORITHM WITH RELAXATION FACTOR FOR THE CAUCHY PROBLEM OF TIME-FRACTIONAL DIFFUSION EQUATION

Zhenping Li; Xiangtuan Xiong

doi:10.11948/20240354

2025 Volume 15 Issue 5

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Zhenping Li, Xiangtuan Xiong. A NEW ITERATION ALGORITHM WITH RELAXATION FACTOR FOR THE CAUCHY PROBLEM OF TIME-FRACTIONAL DIFFUSION EQUATION[J]. Journal of Applied Analysis & Computation, 2025, 15(5): 2959-2976. doi: 10.11948/20240354

Citation:

Zhenping Li, Xiangtuan Xiong. A NEW ITERATION ALGORITHM WITH RELAXATION FACTOR FOR THE CAUCHY PROBLEM OF TIME-FRACTIONAL DIFFUSION EQUATION[J]. Journal of Applied Analysis & Computation, 2025, 15(5): 2959-2976. doi: 10.11948/20240354

A NEW ITERATION ALGORITHM WITH RELAXATION FACTOR FOR THE CAUCHY PROBLEM OF TIME-FRACTIONAL DIFFUSION EQUATION

Zhenping Li^1,3,,
Xiangtuan Xiong^2, ,

1.
Department of Mathematics and Physics, Luoyang Institute of Science and Technology, Luoyang, Henan 471023, China
2.
Department of Mathematics, Northwest Normal University, Lanzhou, Gansu 730070, China
3.
Henan Key Laboratory of Green Building Materials Manufacturing and Intelligent Equipment, Luoyang Institute of Science and Technology, Luoyang, Henan 471023, China

Author Bio: Email: henanlizhp@163.com(Z. Li)
Corresponding author: Email: xiangtuanxion@nwnu.edu.cn(X. Xiong)
Fund Project: The authors were supported by National Natural Science Foundation of China (No. 11661072) and the Natural Science Foundation of Northwest Normal University (No. NWNU-LKQN-17-5)

Abstract

Abstract

In this paper, we investigate a Cauchy problem for the time-fractional diffusion equation by using a new simplified iteration algorithm. The algorithm arises from the well-known Kozlov-Maz'ya iterative scheme for solving the Cauchy problem of classical ill-posed boundary value problems. A relaxation factor in the algorithm is introduced. Based on Fourier analysis, we give a choice rule for the relaxation factor. The iteration algorithm combined with a stopping criterion is given for stable numerical reconstruction of the solution. For illustration, several numerical experiments are constructed to demonstrate the feasibility and efficiency of the proposed method.
- Time-fractional diffusion equation /
- Cauchy problem /
- ill-posedness /
- iterative algorithm /
- stopping criterion
MSC: 35R25, 47A52, 35R30

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References

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