Bivariate rational approximations of the general temperature integral
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929633223507968 |
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| author | Aghili, Alireza Sukhorukova, Nadezda Ugon, Julien |
| author_facet | Aghili, Alireza Sukhorukova, Nadezda Ugon, Julien |
| contents | The non-isothermal analysis of materials with the application of the Arrhenius equation involves temperature integration. If the frequency factor in the Arrhenius equation depends on temperature with a power-law relationship, the integral is known as the general temperature integral. This integral which has no analytical solution is estimated by the approximation functions with different accuracies. In this article, the rational approximations of the integral were obtained based on the minimization of the maximal deviation of bivariate functions. Mathematically, these problems belong to the class of quasiconvex optimization and can be solved using the bisection method. The approximations obtained in this study are more accurate than all approximates available in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_11781 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bivariate rational approximations of the general temperature integral Aghili, Alireza Sukhorukova, Nadezda Ugon, Julien Optimization and Control 90C26, 90C90, 90C47, 65D15, 65K10, 80A30 The non-isothermal analysis of materials with the application of the Arrhenius equation involves temperature integration. If the frequency factor in the Arrhenius equation depends on temperature with a power-law relationship, the integral is known as the general temperature integral. This integral which has no analytical solution is estimated by the approximation functions with different accuracies. In this article, the rational approximations of the integral were obtained based on the minimization of the maximal deviation of bivariate functions. Mathematically, these problems belong to the class of quasiconvex optimization and can be solved using the bisection method. The approximations obtained in this study are more accurate than all approximates available in the literature. |
| title | Bivariate rational approximations of the general temperature integral |
| topic | Optimization and Control 90C26, 90C90, 90C47, 65D15, 65K10, 80A30 |
| url | https://arxiv.org/abs/2412.11781 |