Accuracy and stability are the main properties that make an algorithm preferable to its counterparts in modelling of physical phenomena. The radial basis function collocation method is a novel meshless technique, which exhibits an exponential convergence rate for the numerical solution of partial differential equations. However, it is a global approximation scheme and the illconditioning of the collocation matrix may become a serious issue if dense sets of interpolation nodes or high values of shape parameters are utilized. This study discusses four strategies to improve the accuracy and stability of the radial basis function collocation method for the numerical solution of the multigroup neutron diffusion equation. These strategies include using a higher precision value for computations, utilizing higher exponents for the generalized multiquadric, decreasing the value of the shape parameter with the number of nodes and singular value decomposition filtering. The results have shown that by using a higher precision value, choosing a variable shape parameter strategy and filtering the smallest singular values of the collocation matrix it is possible to improve the performance of the meshless collocation method, while increasing the exponent of the multiquadric results in a more accurate but less stable algorithm.
Birincil Dil  en 

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Bibtex  @araştırma makalesi { jise449391,
journal = {Journal of Innovative Science and Engineering (JISE)},
issn = {},
eissn = {26024217},
address = {Bursa Teknik Üniversitesi},
year = {2018},
volume = {2},
pages = {8  18},
doi = {},
title = {On the Accuracy and Stability of the Meshless RBF Collocation Method for Neutron Diffusion Calculations},
key = {cite},
author = {Tanbay, Tayfun}
} 
APA  Tanbay, T . (2018). On the Accuracy and Stability of the Meshless RBF Collocation Method for Neutron Diffusion Calculations. Journal of Innovative Science and Engineering (JISE), 2 (1), 818. Retrieved from http://jise.btu.edu.tr/issue/38672/449391 
MLA  Tanbay, T . "On the Accuracy and Stability of the Meshless RBF Collocation Method for Neutron Diffusion Calculations". Journal of Innovative Science and Engineering (JISE) 2 (2018): 818 <http://jise.btu.edu.tr/issue/38672/449391> 
Chicago  Tanbay, T . "On the Accuracy and Stability of the Meshless RBF Collocation Method for Neutron Diffusion Calculations". Journal of Innovative Science and Engineering (JISE) 2 (2018): 818 
RIS  TY  JOUR T1  On the Accuracy and Stability of the Meshless RBF Collocation Method for Neutron Diffusion Calculations AU  Tayfun Tanbay Y1  2018 PY  2018 N1  DO  T2  Journal of Innovative Science and Engineering (JISE) JF  Journal JO  JOR SP  8 EP  18 VL  2 IS  1 SN  26024217 M3  UR  Y2  2018 ER  
EndNote  %0 Journal of Innovative Science and Engineering (JISE) On the Accuracy and Stability of the Meshless RBF Collocation Method for Neutron Diffusion Calculations %A Tayfun Tanbay %T On the Accuracy and Stability of the Meshless RBF Collocation Method for Neutron Diffusion Calculations %D 2018 %J Journal of Innovative Science and Engineering (JISE) %P 26024217 %V 2 %N 1 %R %U 
ISNAD  Tanbay, Tayfun . "On the Accuracy and Stability of the Meshless RBF Collocation Method for Neutron Diffusion Calculations". Journal of Innovative Science and Engineering (JISE) 2 / 1 (Haziran 2018): 818. 