Asymptotically Compatible Fractional Grönwall Inequality and its Applications
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916229580587008 |
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| author | Yin, Daopeng Mei, Liquan |
| author_facet | Yin, Daopeng Mei, Liquan |
| contents | In this work, we will give proper estimates for the discrete convolution complementary (DCC) kernels, which leads to the asymptotically compatible fractional Grönwall inequality. The consequence can be applied in the analysis of the stability and pointwise-in-time error of difference-type schemes on a non-uniform mesh. The pointwise error is explicitly bound when a non-uniform time grid is given by a specific scale function e.g. graded mesh, can be given directly. Numerical experiments towards the conclusion of this work validate the error analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_19170 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotically Compatible Fractional Grönwall Inequality and its Applications Yin, Daopeng Mei, Liquan Numerical Analysis 34A08, 35R11, 35A35, 45L05 G.1.8; G.1.7; G.1.4 In this work, we will give proper estimates for the discrete convolution complementary (DCC) kernels, which leads to the asymptotically compatible fractional Grönwall inequality. The consequence can be applied in the analysis of the stability and pointwise-in-time error of difference-type schemes on a non-uniform mesh. The pointwise error is explicitly bound when a non-uniform time grid is given by a specific scale function e.g. graded mesh, can be given directly. Numerical experiments towards the conclusion of this work validate the error analysis. |
| title | Asymptotically Compatible Fractional Grönwall Inequality and its Applications |
| topic | Numerical Analysis 34A08, 35R11, 35A35, 45L05 G.1.8; G.1.7; G.1.4 |
| url | https://arxiv.org/abs/2404.19170 |