On the solution existence for collocation discretizations of time-fractional subdiffusion equations
| Autor: | Franz, Sebastian, Kopteva, Natalia |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Time-fractional parabolic equations with a Caputo time derivative of order $\alpha\in(0,1)$ are discretized in time using continuous collocation methods. For such discretizations, we give sufficient conditions for existence and uniqueness of their solutions. Two approaches are explored: the Lax-Milgram Theorem and the eigenfunction expansion. The resulting sufficient conditions, which involve certain $m\times m$ matrices (where $m$ is the order of the collocation scheme), are verified both analytically, for all $m\ge 1$ and all sets of collocation points, and computationally, for all $ m\le 20$. The semilinear case is also addressed. Comment: 18 pages, 3 figures |
| Databáze: | arXiv |
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