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Mohammad, Anber Abraheem Shlash, Mohammad, Suleiman Ibrahim, Vasudevan, Asokan, Alshurideh, Muhammad Turki, Nan, Ding. (1404). On the numerical solution of the Bagley-Torvik equation using the M\"{u}ntz-Legendre wavelet collocation method. سامانه مدیریت نشریات علمی, 13(3), 968-979. doi: 10.22034/cmde.2025.65631.3029
Anber Abraheem Shlash Mohammad; Suleiman Ibrahim Mohammad; Asokan Vasudevan; Muhammad Turki Alshurideh; Ding Nan. "On the numerical solution of the Bagley-Torvik equation using the M\"{u}ntz-Legendre wavelet collocation method". سامانه مدیریت نشریات علمی, 13, 3, 1404, 968-979. doi: 10.22034/cmde.2025.65631.3029
Mohammad, Anber Abraheem Shlash, Mohammad, Suleiman Ibrahim, Vasudevan, Asokan, Alshurideh, Muhammad Turki, Nan, Ding. (1404). 'On the numerical solution of the Bagley-Torvik equation using the M\"{u}ntz-Legendre wavelet collocation method', سامانه مدیریت نشریات علمی, 13(3), pp. 968-979. doi: 10.22034/cmde.2025.65631.3029
Mohammad, Anber Abraheem Shlash, Mohammad, Suleiman Ibrahim, Vasudevan, Asokan, Alshurideh, Muhammad Turki, Nan, Ding. On the numerical solution of the Bagley-Torvik equation using the M\"{u}ntz-Legendre wavelet collocation method. سامانه مدیریت نشریات علمی, 1404; 13(3): 968-979. doi: 10.22034/cmde.2025.65631.3029

On the numerical solution of the Bagley-Torvik equation using the M\"{u}ntz-Legendre wavelet collocation method

Computational Methods for Differential Equations
مقاله 17، دوره 13، شماره 3، مهر 2025، صفحه 968-979    اصل مقاله (497.89 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2025.65631.3029
نویسندگان
Anber Abraheem Shlash Mohammad1؛ Suleiman Ibrahim Mohammad* 2؛ Asokan Vasudevan3؛ Muhammad Turki Alshurideh4؛ Ding Nan5
1Digital Marketing Department, Faculty of Administrative and Financial Sciences, Petra University, Jordan.
2Electronic Marketing and Social Media, Economic and Administrative Sciences Zarqa University, Jordan.
3Faculty of Business and Communications, INTI International University, 71800 Negeri Sembilan, Malaysia.
4Department of Marketing, School of Business, The University of Jordan, Amman, Jordan.
5Faculty of Liberal Arts, Shinawatra University, Thailand.
چکیده
 The main goals of this work are to solve the Bagley–Torvik (BT) equation using an effective scheme and to find its numerical solution. The scheme uses the collocation method based on the Müntz-Legendre (ML) wavelets. To apply the method, after approximating the unknown solution by mapping it to the wavelet space, we replace it in the desired equation and then obtain the residual using the operational matrices of the derivative and the Caputo
fractional derivative (CFD).
Applying the collocation method results in a linear algebraic system. To implement the collocation method, either Chebyshev or Legendre roots serve as collocation points, or uniformly spaced grids are used. The error analysis is investigated, and some numerical examples are presented to show the scheme’s accuracy and effectiveness. Thanks to the flexibility of ML wavelets and the method’s structure, we can sometimes obtain the exact solution.
کلیدواژه‌ها
Fractional differential equation؛ Wavelet collocation method؛ Müntz-Legendre wavelets؛ Bagley–Torvik equation
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