Identification of the Initial Value for a Time-Fractional Diffusion Equation
Abstract
:1. Introduction
2. Auxiliary Results
3. The Exact Solution and Regularization Strategies
4. Estimate for the a Priori Rule
5. Estimate for a Posteriori Rule
- (a)
- is a continuous function;
- (b)
- (c)
- (d)
- is a strictly decreasing function.
6. Numerical Examples
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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K | 5 | 10 | 15 | 20 | 25 | 30 | 35 |
Relative error | 0.1968 | 0.0993 | 0.1326 | 0.1433 | 0.1665 | 0.1602 | 0.1772 |
M | 5 | 10 | 15 | 20 | 25 | 30 | 35 |
Relative error | 0.1602 | 0.0993 | 0.2822 | 0.4498 | 0.5678 | 0.6043 | 0.7543 |
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Yang, F.; Gao, Y.-X.; Li, D.-G.; Li, X.-X. Identification of the Initial Value for a Time-Fractional Diffusion Equation. Symmetry 2022, 14, 2569. https://doi.org/10.3390/sym14122569
Yang F, Gao Y-X, Li D-G, Li X-X. Identification of the Initial Value for a Time-Fractional Diffusion Equation. Symmetry. 2022; 14(12):2569. https://doi.org/10.3390/sym14122569
Chicago/Turabian StyleYang, Fan, Yin-Xia Gao, Dun-Gang Li, and Xiao-Xiao Li. 2022. "Identification of the Initial Value for a Time-Fractional Diffusion Equation" Symmetry 14, no. 12: 2569. https://doi.org/10.3390/sym14122569
APA StyleYang, F., Gao, Y.-X., Li, D.-G., & Li, X.-X. (2022). Identification of the Initial Value for a Time-Fractional Diffusion Equation. Symmetry, 14(12), 2569. https://doi.org/10.3390/sym14122569