A note on the L1 discretization error for the Caputo derivative in Hölder spaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866915024219406336 |
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| author | del Teso, Félix Płociniczak, Łukasz |
| author_facet | del Teso, Félix Płociniczak, Łukasz |
| contents | We establish uniform error bounds of the L1 discretization of the Caputo derivative of Hölder continuous functions. The result can be understood as: error = (degree of smoothness - order of the derivative). We present an elementary proof and illustrate its optimality with numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_10833 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on the L1 discretization error for the Caputo derivative in Hölder spaces del Teso, Félix Płociniczak, Łukasz Numerical Analysis We establish uniform error bounds of the L1 discretization of the Caputo derivative of Hölder continuous functions. The result can be understood as: error = (degree of smoothness - order of the derivative). We present an elementary proof and illustrate its optimality with numerical examples. |
| title | A note on the L1 discretization error for the Caputo derivative in Hölder spaces |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2411.10833 |