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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, (), -. 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, , , 1400, -. 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, (), pp. -. 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; (): -. 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
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 24 خرداد 1400  XML اصل مقاله (444.3 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2021.44736.1890
نویسندگان
Asadollah Torabi Giklouorcid 1، 2؛ Mojtaba Ranjbar email orcid 3، 4؛ Mahmoud Shafieeorcid 2؛ 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 Finance Sciences, Kharazmi University, Tehran, Iran.
چکیده
In this article, we use the collocation method based on the radial basis functions with sym-
metric variable shape parameter (SVSP) to obtain numerical solutions of neutral-type functional-
differential equations with proportional delays. We used Gaussian radial basis functions with SVSP.
Using non uniform collocation points, we achieved a system and solving this system yielded the prob-
lem solutions. 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). Finally, numerical rate of convergence
analysis of the numerical approximation was also obtained. It is observed that by comparing be-
tween the obtained ROC values of error norms by the SVSP and CSP method, SVSP results were
considered acceptable.
کلیدواژه‌ها
functional-differential equation؛ proportional delay؛ radial basis function؛ variable shape parameter
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