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

Document Type : Research Paper

Authors

1 Digital Marketing Department, Faculty of Administrative and Financial Sciences, Petra University, Jordan.

2 Electronic Marketing and Social Media, Economic and Administrative Sciences Zarqa University, Jordan.

3 Faculty of Business and Communications, INTI International University, 71800 Negeri Sembilan, Malaysia.

4 Department of Marketing, School of Business, The University of Jordan, Amman, Jordan.

5 Faculty of Liberal Arts, Shinawatra University, Thailand.

Abstract

 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.

Keywords

Main Subjects

Computational Methods for Differential Equations
Volume 13, Issue 3
July 2025
Pages 968-979

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History

  • Receive Date: 25 January 2025
  • Revise Date: 09 February 2025
  • Accept Date: 22 February 2025

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