Shooting Methods for Fractional Dirichlet-Type Boundary Value Problems of Order $\alpha \in (1,2)$ With Caputo Derivatives
<|reference_start|>Shooting Methods for Fractional Dirichlet-Type Boundary Value Problems of Order $\alpha \in (1,2)$ With Caputo Derivatives: For the numerical solution of Dirichlet-type boundary value problems associated to nonlinear fractional differential equations of order $\alpha \in (1,2)$ 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.<|reference_end|>
@article{diethelm2024shooting,
    title={Shooting Methods for Fractional Dirichlet-Type Boundary Value Problems
  of Order $\alpha \in (1,2)$ With Caputo Derivatives},
    author={Kai Diethelm},
    journal={arXiv preprint arXiv:2402.03487},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.03487},
    primaryClass={math.NA cs.NA}
}