ON THE NUMERICAL SOLUTION OF BAGLEY-TORVIK EQUATION USING THE M ¨UNTZ-LEGENDRE WAVELET COLLOCATION METHOD

Articles in Press

Document Type : Research Paper

Authors

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

2 1. Electronic Marketing and Social Media, Economic and Administrative Sciences Zarqa University, Jordan. 2. Research follower, INTI International University, 71800 Negeri Sembilan, Malaysia.

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

Solving the Bagley–Torvik (BT) equation using an effective scheme and finding its numerical solution are the main goals of this work. The scheme benefits the collocation method based on the M¨untz Legendre wavelets (ML). To apply the method, after approximating the unknown solution by mapping it in the wavelet space, we replace it in the desired equation and then obtain the residual using the operational matrices of the derivative and Caputo fractional derivative (CFD). Applying the collocation method results in a linear algebraic system. To implement the collocation method, either Chebyshev or Legendre roots are used as collocation points or uniformly spaced grids are selected. The error analysis is investigated, and some numerical examples are presented to show the accuracy and effectiveness of the scheme. Thanks to the flexibility of M¨untz-Legendre wavelets, and the method’s structure, we can even obtain the exact solution in some cases

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 01 March 2025

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History

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

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