Analysis and implementation of collocation methods for fractional differential equations
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909707705253888 |
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| author | Brugnano, Luigi Gurioli, Gianmarco Iavernaro, Felice Vikerpuur, Mikk |
| author_facet | Brugnano, Luigi Gurioli, Gianmarco Iavernaro, Felice Vikerpuur, Mikk |
| contents | Recently, the class of Runge-Kutta type methods named Fractional HBVMs (FHBVMs) has been introduced for the numerical solution of initial value problems of fractional differential equations, and a corresponding Matlab software has been released. Though an error analysis has already been given, a corresponding linear stability analysis is still lacking. We here provide such an analysis, together with some improvements concerning the mesh selection. This latter has been implemented into a new version of the code, which is available on the web. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_17719 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analysis and implementation of collocation methods for fractional differential equations Brugnano, Luigi Gurioli, Gianmarco Iavernaro, Felice Vikerpuur, Mikk Numerical Analysis 34A08, 65R20, 65-04 Recently, the class of Runge-Kutta type methods named Fractional HBVMs (FHBVMs) has been introduced for the numerical solution of initial value problems of fractional differential equations, and a corresponding Matlab software has been released. Though an error analysis has already been given, a corresponding linear stability analysis is still lacking. We here provide such an analysis, together with some improvements concerning the mesh selection. This latter has been implemented into a new version of the code, which is available on the web. |
| title | Analysis and implementation of collocation methods for fractional differential equations |
| topic | Numerical Analysis 34A08, 65R20, 65-04 |
| url | https://arxiv.org/abs/2503.17719 |