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.
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Ghasemi, A., & Saadatmandi, A. (2024). A new Bernstein-reproducing kernel method for solving forced Duffing equations with integral boundary conditions. Computational Methods for Differential Equations, 12(2), 329-337. doi: 10.22034/cmde.2023.57413.2401
MLA
Azam Ghasemi; Abbas Saadatmandi. "A new Bernstein-reproducing kernel method for solving forced Duffing equations with integral boundary conditions". Computational Methods for Differential Equations, 12, 2, 2024, 329-337. doi: 10.22034/cmde.2023.57413.2401
HARVARD
Ghasemi, A., Saadatmandi, A. (2024). 'A new Bernstein-reproducing kernel method for solving forced Duffing equations with integral boundary conditions', Computational Methods for Differential Equations, 12(2), pp. 329-337. doi: 10.22034/cmde.2023.57413.2401
VANCOUVER
Ghasemi, A., Saadatmandi, A. A new Bernstein-reproducing kernel method for solving forced Duffing equations with integral boundary conditions. Computational Methods for Differential Equations, 2024; 12(2): 329-337. doi: 10.22034/cmde.2023.57413.2401
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