Advantages of the Discrete Stochastic Arithmetic to Validate the Results of the Taylor Expansion Method to Solve the Generalized Abel’s Integral Equation
| Autor: | Samad Noeiaghdam, Eisa Zarei |
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| Rok vydání: | 2021 |
| Předmět: |
Physics and Astronomy (miscellaneous)
Computer science General Mathematics Taylor expansion method 010103 numerical & computational mathematics 01 natural sciences Volterra integral equation Stochastic arithmetic symbols.namesake Approximation error Error analysis CESTAC method QA1-939 Computer Science (miscellaneous) Taylor series Applied mathematics 0101 mathematics Discrete Stochastic Arithmetic generalized Abel’s integral equation 010102 general mathematics Integral equation Chemistry (miscellaneous) Kernel (statistics) symbols CADNA library Mathematics |
| Zdroj: | Symmetry Volume 13 Issue 8 Symmetry, Vol 13, Iss 1370, p 1370 (2021) |
| ISSN: | 2073-8994 |
| DOI: | 10.3390/sym13081370 |
| Popis: | The aim of this paper is to apply the Taylor expansion method to solve the first and second kinds Volterra integral equations with Abel kernel. This study focuses on two main arithmetics: the FPA and the DSA. In order to apply the DSA, we use the CESTAC method and the CADNA library. Using this method, we can find the optimal step of the method, the optimal approximation, the optimal error, and some of numerical instabilities. They are the main novelties of the DSA in comparison with the FPA. The error analysis of the method is proved. Furthermore, the main theorem of the CESTAC method is presented. Using this theorem we can apply a new termination criterion instead of the traditional absolute error. Several examples are approximated based on the FPA and the DSA. The numerical results show the applications and advantages of the DSA than the FPA. |
| Databáze: | OpenAIRE |
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