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Ghasemi, Azam, Saadatmandi, Abbas. (1402). A new Bernstein-reproducing kernel method for solving forced Duffing equations with integral boundary conditions. سامانه مدیریت نشریات علمی, 12(2), 329-337. doi: 10.22034/cmde.2023.57413.2401
Azam Ghasemi; Abbas Saadatmandi. "A new Bernstein-reproducing kernel method for solving forced Duffing equations with integral boundary conditions". سامانه مدیریت نشریات علمی, 12, 2, 1402, 329-337. doi: 10.22034/cmde.2023.57413.2401
Ghasemi, Azam, Saadatmandi, Abbas. (1402). 'A new Bernstein-reproducing kernel method for solving forced Duffing equations with integral boundary conditions', سامانه مدیریت نشریات علمی, 12(2), pp. 329-337. doi: 10.22034/cmde.2023.57413.2401
Ghasemi, Azam, Saadatmandi, Abbas. A new Bernstein-reproducing kernel method for solving forced Duffing equations with integral boundary conditions. سامانه مدیریت نشریات علمی, 1402; 12(2): 329-337. doi: 10.22034/cmde.2023.57413.2401

A new Bernstein-reproducing kernel method for solving forced Duffing equations with integral boundary conditions

Computational Methods for Differential Equations
مقاله 9، دوره 12، شماره 2، خرداد 2024، صفحه 329-337    اصل مقاله (360.34 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2023.57413.2401
نویسندگان
Azam Ghasemi؛ Abbas Saadatmandi*
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, Iran.
چکیده
In the current work, a new reproducing kernel method (RKM) for solving nonlinear forced Duffing equations with integral boundary conditions is developed. The proposed collocation technique is based on the idea of RKM and the orthonormal Bernstein polynomials (OBPs) approximation together with the quasi-linearization method. In our method, contrary to the classical RKM, there is no need to use the Gram-Schmidt orthogonalization procedure and only a few nodes are used to obtain efficient numerical results. Three numerical examples are included to show the applicability and efficiency of the suggested method. Also, the obtained numerical results are compared with some results in the literature.
کلیدواژه‌ها
Duffing equations؛ Integral boundary conditions؛ Reproducing kernel method؛ Bernstein polynomials؛ Quasi-linearization method
مراجع
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