Shooting Methods for Fractional Dirichlet-Type Boundary Value Problems of Order $α\in (1,2)$ With Caputo Derivatives
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916824622301184 |
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| author | Diethelm, Kai |
| author_facet | Diethelm, Kai |
| contents | For the numerical solution of Dirichlet-type boundary value problems associated to nonlinear fractional differential equations of order $α\in (1,2)$ that use Caputo derivatives, we suggest to employ shooting methods. In particular, we demonstrate that the so-called proportional secting technique for selecting the required initial values leads to numerical schemes that converge to high accuracy in a very small number of shooting iterations, and we provide an explanation of the analytical background for this favourable numerical behaviour. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_03487 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Shooting Methods for Fractional Dirichlet-Type Boundary Value Problems of Order $α\in (1,2)$ With Caputo Derivatives Diethelm, Kai Numerical Analysis Primary 65L10, Secondary 34A08, 65R20 For the numerical solution of Dirichlet-type boundary value problems associated to nonlinear fractional differential equations of order $α\in (1,2)$ that use Caputo derivatives, we suggest to employ shooting methods. In particular, we demonstrate that the so-called proportional secting technique for selecting the required initial values leads to numerical schemes that converge to high accuracy in a very small number of shooting iterations, and we provide an explanation of the analytical background for this favourable numerical behaviour. |
| title | Shooting Methods for Fractional Dirichlet-Type Boundary Value Problems of Order $α\in (1,2)$ With Caputo Derivatives |
| topic | Numerical Analysis Primary 65L10, Secondary 34A08, 65R20 |
| url | https://arxiv.org/abs/2402.03487 |