A spectrally accurate step-by-step method for the numerical solution of fractional differential equations
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916197049565184 |
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| author | Brugnano, L. Burrage, K. Burrage, P. Iavernaro, F. |
| author_facet | Brugnano, L. Burrage, K. Burrage, P. Iavernaro, F. |
| contents | In this paper we consider the numerical solution of fractional differential equations. In particular, we study a step-by-step graded mesh procedure based on an expansion of the vector field using orthonormal Jacobi polynomials. Under mild hypotheses, the proposed procedure is capable of getting spectral accuracy. A few numerical examples are reported to confirm the theoretical findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_10526 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A spectrally accurate step-by-step method for the numerical solution of fractional differential equations Brugnano, L. Burrage, K. Burrage, P. Iavernaro, F. Numerical Analysis 65L05, 65L03, 65L99 In this paper we consider the numerical solution of fractional differential equations. In particular, we study a step-by-step graded mesh procedure based on an expansion of the vector field using orthonormal Jacobi polynomials. Under mild hypotheses, the proposed procedure is capable of getting spectral accuracy. A few numerical examples are reported to confirm the theoretical findings. |
| title | A spectrally accurate step-by-step method for the numerical solution of fractional differential equations |
| topic | Numerical Analysis 65L05, 65L03, 65L99 |
| url | https://arxiv.org/abs/2310.10526 |