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Torabi Giklou, Asadollah, Ranjbar, Mojtaba, Shafiee, Mahmoud, Roomi, Vahid. (1400). Collocation method based on radial basis functions via symmetric variable shape parameter for solving a particular class of delay differential equations. سامانه مدیریت نشریات علمی, 10(1), 144-157. doi: 10.22034/cmde.2021.44736.1890
Asadollah Torabi Giklou; Mojtaba Ranjbar; Mahmoud Shafiee; Vahid Roomi. "Collocation method based on radial basis functions via symmetric variable shape parameter for solving a particular class of delay differential equations". سامانه مدیریت نشریات علمی, 10, 1, 1400, 144-157. doi: 10.22034/cmde.2021.44736.1890
Torabi Giklou, Asadollah, Ranjbar, Mojtaba, Shafiee, Mahmoud, Roomi, Vahid. (1400). 'Collocation method based on radial basis functions via symmetric variable shape parameter for solving a particular class of delay differential equations', سامانه مدیریت نشریات علمی, 10(1), pp. 144-157. doi: 10.22034/cmde.2021.44736.1890
Torabi Giklou, Asadollah, Ranjbar, Mojtaba, Shafiee, Mahmoud, Roomi, Vahid. Collocation method based on radial basis functions via symmetric variable shape parameter for solving a particular class of delay differential equations. سامانه مدیریت نشریات علمی, 1400; 10(1): 144-157. doi: 10.22034/cmde.2021.44736.1890

Collocation method based on radial basis functions via symmetric variable shape parameter for solving a particular class of delay differential equations

Computational Methods for Differential Equations
مقاله 10، دوره 10، شماره 1، فروردین 2022، صفحه 144-157    اصل مقاله (371.27 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2021.44736.1890
نویسندگان
Asadollah Torabi Giklou1، 2؛ Mojtaba Ranjbar* 3، 4؛ Mahmoud Shafiee2؛ Vahid Roomi3
1Department of Mathematics, Guilan Science and Research Branch, Islamic Azad University, Rasht, Iran.
2Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran.
3Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.
4Faculty of Financial Sciences, Kharazmi University, Tehran, Iran.
چکیده
In this article, we use the collocation method based on the radial basis functions with symmetric variable shape parameter (SVSP) to obtain numerical solutions of neutral-type functional-differential equations with proportional delays. In this method, we control the absolute errors and the condition number of the system matrix through the program prepared with Maple 18.0 by increasing the number of collocation points that have a direct effect on the defined shape parameter. Also, we present the tables of the rate of the convergence (ROC) to investigate and show the convergence rate of this method compared to the RBF method with constant shape parameter. Several examples are given to illustrate the efficiency and accuracy of the introduced method in comparison with the same method with the constant shape parameter (CSP) as well as other analytical and numerical methods. Comparison of the obtained numerical results shows the considerable superiority of the collocation method based on RBFs with SVSP in accuracy and convergence over the collocation method based on the RBFs with CSP and other analytical and numerical methods for delay differential equations (DDEs).
کلیدواژه‌ها
Functional-differential equation؛ Proportional delay؛ Radial basis function؛ Variable shape parameter
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