A new approach to shooting methods for terminal value problems of fractional differential equations
| Title: | A new approach to shooting methods for terminal value problems of fractional differential equations |
|---|---|
| Authors: | Diethelm, Kai, Uhlig, Frank |
| Source: | J. Sci. Comput. 97 (2023), Article No. 38 |
| Publication Year: | 2023 |
| Collection: | Computer Science Mathematics |
| Subject Terms: | Mathematics - Numerical Analysis, Primary 65L10, Secondary 34A08, 65R20 |
| More Details: | For terminal value problems of fractional differential equations of order $\alpha \in (0,1)$ that use Caputo derivatives, shooting methods are a well developed and investigated approach. Based on recently established analytic properties of such problems, we develop a new technique to select the required initial values that solves such shooting problems quickly and accurately. Numerical experiments indicate that this new proportional secting technique converges very quickly and accurately to the solution. Run time measurements indicate a speedup factor of between 4 and 10 when compared to the standard bisection method. Comment: 27 pages, 1 figure. The software described in this paper can be downloaded from https://doi.org/10.5281/zenodo.7678311 |
| Document Type: | Working Paper |
| DOI: | 10.1007/s10915-023-02361-9 |
| Access URL: | http://arxiv.org/abs/2303.15454 |
| Accession Number: | edsarx.2303.15454 |
| Database: | arXiv |
| DOI: | 10.1007/s10915-023-02361-9 |
|---|