Combining arbitrary order global Padé approximation of the Mittag-Leffler function with its addition formula for a significant accuracy boost
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913473121746944 |
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| author | Herrmann, Richard |
| author_facet | Herrmann, Richard |
| contents | The combination of the global Padé approximation of the Mittag-Leffler function with its addition formula for the case $α<1$ yields significantly higher accuracy results for a given arbitrary order $n$. We present a solution in terms of a Mathematica notebook to determine the general structure of the system of linear equations to be solved, followed by an implementation as a {\tt{C++}} program using the {\tt{Eigen}} template library for linear algebra. For a comparison with contour integral solutions we present an implementation as a {\tt{C++}} program using the {\tt{boost}} library's quadrature package employing the Gauss-Kronrod-method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_10257 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Combining arbitrary order global Padé approximation of the Mittag-Leffler function with its addition formula for a significant accuracy boost Herrmann, Richard General Physics The combination of the global Padé approximation of the Mittag-Leffler function with its addition formula for the case $α<1$ yields significantly higher accuracy results for a given arbitrary order $n$. We present a solution in terms of a Mathematica notebook to determine the general structure of the system of linear equations to be solved, followed by an implementation as a {\tt{C++}} program using the {\tt{Eigen}} template library for linear algebra. For a comparison with contour integral solutions we present an implementation as a {\tt{C++}} program using the {\tt{boost}} library's quadrature package employing the Gauss-Kronrod-method. |
| title | Combining arbitrary order global Padé approximation of the Mittag-Leffler function with its addition formula for a significant accuracy boost |
| topic | General Physics |
| url | https://arxiv.org/abs/2408.10257 |