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The use of CESTAC method to find optimal shape parameter and optimal number of points in RBF-meshless methods to solve differential equations | ||
| Computational Methods for Differential Equations | ||
| مقاله 6، دوره 8، شماره 4، بهمن 2020، صفحه 685-707 اصل مقاله (2.8 MB) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2020.27817.1374 | ||
| نویسندگان | ||
Hasan Barzegar Kelishami؛ Mohammad Ali Fariborzi Araghi  ؛ Majid Amirfakhrian
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| Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran. | ||
| چکیده | ||
| One of the schemes to find the optimal shape parameter and optimal number of points in the radial basis function (RBF) methods is to apply the stochastic arithmetic (SA) in place of the common floating-point arithmetic (FPA). The main purpose of this work is to introduce a reliable approach based on this new arithmetic to compute the local optimal shape parameter and number of points in multiquadric and Gaussian RBF-meshless methods for solving differential equations, in the iterative process. To this end, the CESTAC method is applied. Also, in order to implement the proposed algorithms, the CADNA library is performed. The examples illustrate the efficiency and importance of using this library to validate the results. | ||
| کلیدواژهها | ||
| Stochastic Arithmetic؛ CESTAC method؛ CADNA library؛ Differential equation؛ Radial basis function (RBF) | ||
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آمار تعداد مشاهده مقاله: 367 تعداد دریافت فایل اصل مقاله: 264 |
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