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## On the Accuracy and Stability of the Meshless RBF Collocation Method for Neutron Diffusion Calculations

#### Tayfun TANBAY [1]

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 ill-conditioning 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.

Meshless method, RBF collocation, Neutron diffusion, Accuracy, Stability
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Birincil Dil en Research Articles Yazar: Tayfun TANBAY (Sorumlu Yazar)Kurum: BURSA TECHNICAL UNIVERSITYÜlke: Turkey Yayımlanma Tarihi : 20 Haziran 2018
 Bibtex @araştırma makalesi { jise449391, journal = {Journal of Innovative Science and Engineering}, issn = {}, eissn = {2602-4217}, address = {ursa Technical University, Mimar Sinan Campus, Mimar Sinan Mah. Mimar Sinan Blv. Eflak Cad. No:177 16310 Yıldırım, Bursa / Turkey}, publisher = {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 , 2 (1) , 8-18 . Retrieved from http://jise.btu.edu.tr/tr/pub/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 2 (2018 ): 8-18 Chicago Tanbay, T . "On the Accuracy and Stability of the Meshless RBF Collocation Method for Neutron Diffusion Calculations". Journal of Innovative Science and Engineering 2 (2018 ): 8-18 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 JF - Journal JO - JOR SP - 8 EP - 18 VL - 2 IS - 1 SN - -2602-4217 M3 - UR - Y2 - 2018 ER - EndNote %0 Journal of Innovative Science and Engineering 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 %P -2602-4217 %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 2 / 1 (Haziran 2018): 8-18 . AMA Tanbay T . On the Accuracy and Stability of the Meshless RBF Collocation Method for Neutron Diffusion Calculations. JISE. 2018; 2(1): 8-18. Vancouver Tanbay T . On the Accuracy and Stability of the Meshless RBF Collocation Method for Neutron Diffusion Calculations. Journal of Innovative Science and Engineering. 2018; 2(1): 8-18. IEEE T. Tanbay , "On the Accuracy and Stability of the Meshless RBF Collocation Method for Neutron Diffusion Calculations", Journal of Innovative Science and Engineering, c. 2, sayı. 1, ss. 8-18, Haz. 2018

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