Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2509.02465 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908515720757248 |
|---|---|
| author | Aylwin, Ruben Oruc, Göksu Urban, Karsten |
| author_facet | Aylwin, Ruben Oruc, Göksu Urban, Karsten |
| contents | We consider boundary value problems with Riemann-Liouville fractional derivatives of order $s\in (1, 2)$ with non-constant diffusion and reaction coefficients. A variational formulation is derived and analyzed leading to the well-posedness of the continuous problem and its Finite Element discretization. Then, the Reduced Basis Method through a greedy algorithm for parametric diffusion and reaction coefficients is analyzed. Its convergence properties, and in particular the decay of the Kolmogorov $n$-width, are seen to depend on the fractional order $s$. Finally, numerical results confirming our findings are presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_02465 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fractional differential equations: non-constant coefficients, simulation and model reduction Aylwin, Ruben Oruc, Göksu Urban, Karsten Numerical Analysis 26A33, 34K37, 65N30 We consider boundary value problems with Riemann-Liouville fractional derivatives of order $s\in (1, 2)$ with non-constant diffusion and reaction coefficients. A variational formulation is derived and analyzed leading to the well-posedness of the continuous problem and its Finite Element discretization. Then, the Reduced Basis Method through a greedy algorithm for parametric diffusion and reaction coefficients is analyzed. Its convergence properties, and in particular the decay of the Kolmogorov $n$-width, are seen to depend on the fractional order $s$. Finally, numerical results confirming our findings are presented. |
| title | Fractional differential equations: non-constant coefficients, simulation and model reduction |
| topic | Numerical Analysis 26A33, 34K37, 65N30 |
| url | https://arxiv.org/abs/2509.02465 |