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Doostdar, Mohammad Reza, Kazemi, Manochehr, Vahidi, Alireza. (1402). A numerical method for solving the Duffing equation involving both integral and non-integral forcing terms with separated and integral boundary conditions. سامانه مدیریت نشریات علمی, 11(2), 241-253. doi: 10.22034/cmde.2022.50054.2082
Mohammad Reza Doostdar; Manochehr Kazemi; Alireza Vahidi. "A numerical method for solving the Duffing equation involving both integral and non-integral forcing terms with separated and integral boundary conditions". سامانه مدیریت نشریات علمی, 11, 2, 1402, 241-253. doi: 10.22034/cmde.2022.50054.2082
Doostdar, Mohammad Reza, Kazemi, Manochehr, Vahidi, Alireza. (1402). 'A numerical method for solving the Duffing equation involving both integral and non-integral forcing terms with separated and integral boundary conditions', سامانه مدیریت نشریات علمی, 11(2), pp. 241-253. doi: 10.22034/cmde.2022.50054.2082
Doostdar, Mohammad Reza, Kazemi, Manochehr, Vahidi, Alireza. A numerical method for solving the Duffing equation involving both integral and non-integral forcing terms with separated and integral boundary conditions. سامانه مدیریت نشریات علمی, 1402; 11(2): 241-253. doi: 10.22034/cmde.2022.50054.2082

A numerical method for solving the Duffing equation involving both integral and non-integral forcing terms with separated and integral boundary conditions

Computational Methods for Differential Equations
مقاله 3، دوره 11، شماره 2، تیر 2023، صفحه 241-253    اصل مقاله (374.72 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2022.50054.2082
نویسندگان
Mohammad Reza Doostdar* 1؛ Manochehr Kazemi2؛ Alireza Vahidi3
1Department of Mathematics, Zarandieh Branch, Islamic Azad University, Zarandieh, Iran
2Department of Mathematics, Ashtian Branch, Islamic Azad University, Ashtian, Iran
3Department of Mathematics, Yadegar -e-Imam Khomeini (RAH) Shahre Rey Branch, Islamic Azad University, Tehran, Iran
چکیده
This paper presents an efficient numerical method to solve two versions of the Duffing equation by the hybrid functions based on the combination of Block-pulse functions and Legendre polynomials. This method reduces the solution of the considered problem to the solution of a system of algebraic equations. Moreover, the convergence of the method is studied. Some examples are given to demonstrate the applicability and effectiveness of the proposed method. Also, the obtained results are compared with some other results. 
کلیدواژه‌ها
Integral boundary conditions؛ Boundary value problem؛ Duffing equation؛ Hybrid functions؛ Legendre polynomials
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