Shooting methods for fractional Dirichlet-type boundary value problems of order α ∈ (1, 2) with Caputo derivatives
- For the numerical solution of Dirichlet-type boundary value problems associated to nonlinear fractional differential equations of order 𝛼 ∈ (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.
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| Author: | Kai Diethelm |
|---|---|
| URN: | urn:nbn:de:bvb:863-opus-59665 |
| DOI: | https://doi.org/10.1007/978-3-032-00155-9_8 |
| ISBN: | 978-3-032-00154-2 |
| Parent Title (English): | Recent Developments in Operator Theory, Mathematical Physics and Complex Analysis |
| Publisher: | Birkhäuser |
| Place of publication: | Cham |
| Editor: | Joseph Ball, Hans-Olav Tylli, Jani A. Virtanen |
| Document Type: | Conference Proceeding |
| Language: | English |
| Year of publication: | 2025 |
| Publishing Institution: | Technische Hochschule Würzburg-Schweinfurt |
| Release Date: | 2025/07/15 |
| Tag: | Caputo derivative; boundary condition; boundary value problem; fractional differential equation; proportional secting; secant method; shooting method |
| Faculties and institutes: | Fakultäten / Fakultät für angewandte Natur- und Geisteswissenschaften |
| Licence (German): |  Creative Commons - CC BY-NC-ND - Namensnennung - Nicht kommerziell - Keine Bearbeitungen 4.0 International |
