Numerical solution of some class of differential equations by Galerkin method utilizing Boubaker wavelets Galerkin method with Boubaker wavelets
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Abstract
This paper proposes a Galerkin method based on Boubaker wavelets (BWGM) for the numerical solution of a class of differential equations. The method employs Boubaker wavelets as both weight functions and basis elements to construct approximate solutions. The accuracy of the proposed method is evaluated by comparing numerical results with exact solutions and with existing schemes such as the Galerkin method using Fibonacci and Gegenbauer wavelets. Several examples are provided to demonstrate the validity and applicability of the method. The results indicate that BWGM yields high accuracy with minimal absolute error, making it an efficient tool for solving linear, singular, and nonlinear boundary value problems.
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References
K. Amaratunga and J. R. William, Wavelet-Galerkin solutions for one-dimensional partial differential equations, Internat. J. Numer. Methods Engrg. 37 (1994), 2703–2716.
https://doi.org/10.1002/nme.1620371602
L. M. Angadi, Numerical solution of generalized Burgers–Huxley equations using wavelet based lifting schemes, J. Appl. Math. Stat. Anal. 3(2) (2022), 1–14.
https://doi.org/10.5281/zenodo.13682930
L. M. Angadi, Wavelet based Galerkin method for the numerical solution of singular boundary value problems using Fibonacci wavelets, J. Sci. Res. 17(1) (2025), 227–234.
http://dx.doi.org/10.3329/jsr.v17i1.75341
L. M. Angadi, Galerkin method for the numerical solution of some class of differential equations by utilizing Gegenbauer wavelets, J. Innov. Appl. Math. Comput. Sci. 5(1) (2025), 14–24.
http://dx.doi.org/10.58205/jiamcs.v5i1.1914
G. Beylkin, R. Coifman and V. Rokhlin, Fast wavelet transforms and numerical algorithms I, Comm. Pure Appl. Math. 44(2) (1991), 141–183.
https://doi.org/10.1002/cpa.3160440202
J. E. Cicelia, Solution of weighted residual problems by using Galerkin’s method, Indian J. Sci. Technol. 7(3) (2014), 52–54.
https://doi.org/10.17485/ijst/2014/v7sp3.3
I. Daubechies, Orthogonal bases of compactly supported wavelets, Comm. Pure Appl. Math. 41(7) (1988), 909–996.
http://dx.doi.org/10.1002/cpa.3160410705
H. Kaur, R. C. Mittal and R. V. Mishra, Haar wavelet quasilinearization approach for solving nonlinear boundary value problems, Amer. J. Comput. Math. 1 (2011), 176–182.
A. Mohsen and M. El-Gamel, On the Galerkin and collocation methods for two point boundary value problems using sine bases, Comput. Math. Appl. 56(4) (2008), 930–941.
J. W. Mosevich, Identifying differential equations by Galerkin's method, Math. Comp. 31 (1977), 139–147.
https://doi.org/10.2307/2005785
M. A. Sarhan, S. Shihab and M. Rasheed, A new Boubaker wavelets operational matrix of integration, J. Southwest Jiaotong Univ. 55(2) (2020).
S. C. Shiralashetti and A. B. Deshi, Numerical solution of differential equations arising in fluid dynamics using Legendre wavelet collocation method, Int. J. Comput. Mater. Sci. Eng. 6(2) (2017), 1750014.
https://doi.org/10.1142/S2047684117500142
S. C. Shiralashetti, L. M. Angadi and S. Kumbinarasaiah, Laguerre wavelet-Galerkin method for the numerical solution of one-dimensional partial differential equations, Int. J. Math. Appl. 6(1-E) (2018), 939–949.
S. C. Shiralashetti and S. Kumbinarasaiah, Hermite wavelets method for the numerical solution of linear and nonlinear singular initial and boundary value problems, Comput. Methods Differ. Equ. 7(2) (2019), 177–198.
S. C. Shiralashetti and L. Lamani, Boubaker wavelet based numerical method for the solution of Abel's integral equations, Math. Forum 28(2) (2020), 114–124.