Numerical Identification of External Boundary Conditions for Time Fractional Parabolic Equations on Disjoint Domains
Abstract
:1. Introduction
2. Direct and Inverse Problems
3. Existence and Uniqueness of the Solution of the Direct Problem
4. Solution of the Semidiscrete Direct and Inverse Problem
4.1. Time Semidiscretization of the Direct Problem
4.2. Solving the Inverse Problems
5. Numerical Realization
5.1. Full Discretizations
5.2. Correctness
5.3. Implementation
6. Extension to 2D Problem
7. Numerical Simulations
8. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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0.5 | 0.5 | 5.699 | 1.965 | 6.157 | 2.142 | 7.418 | 2.600 | 9.118 | |
1.536 | 1.674 | 1.523 | 1.530 | 1.512 | 1.512 | ||||
1.844 | 6.665 | 2.213 | 7.720 | 2.653 | 9.398 | 3.286 | |||
1.468 | 1.591 | 1.519 | 1.541 | 1.497 | 1.516 | ||||
0.3 | 0.6 | 1.014 | 3.113 | 1.046 | 3.873 | 1.462 | 5.453 | 2.040 | |
1.703 | 1.573 | 1.433 | 1.406 | 1.423 | 1.419 | ||||
3.166 | 1.075 | 3.496 | 1.333 | 4.911 | 1.859 | 6.930 | |||
1.559 | 1.620 | 1.391 | 1.441 | 1.401 | 1.424 | ||||
0.9 | 0.4 | 2.672 | 9.865 | 4.230 | 1.988 | 8.263 | 3.832 | 1.684 | |
1.438 | 1.222 | 1.089 | 1.267 | 1.109 | 1.186 | ||||
9.591 | 3.127 | 1.535 | 6.830 | 2.907 | 1.331 | 6.159 | |||
1.617 | 1.026 | 1.168 | 1.232 | 1.127 | 1.112 |
1.037 | 2.583 | 6.445 | 1.610 | 4.022 | 1.005 | 2.512 | |
2.005 | 2.003 | 2.002 | 2.001 | 2.000 | 2.000 | ||
3.725 | 9.320 | 2.330 | 5.822 | 1.455 | 3.637 | 9.093 | |
1.999 | 2.000 | 2.000 | 2.000 | 2.000 | 2.000 |
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Koleva, M.N.; Vulkov, L.G. Numerical Identification of External Boundary Conditions for Time Fractional Parabolic Equations on Disjoint Domains. Fractal Fract. 2023, 7, 326. https://doi.org/10.3390/fractalfract7040326
Koleva MN, Vulkov LG. Numerical Identification of External Boundary Conditions for Time Fractional Parabolic Equations on Disjoint Domains. Fractal and Fractional. 2023; 7(4):326. https://doi.org/10.3390/fractalfract7040326
Chicago/Turabian StyleKoleva, Miglena N., and Lubin G. Vulkov. 2023. "Numerical Identification of External Boundary Conditions for Time Fractional Parabolic Equations on Disjoint Domains" Fractal and Fractional 7, no. 4: 326. https://doi.org/10.3390/fractalfract7040326