Investigating an Approximate Solution for a Fractional-Order Bagley–Torvik Equation by Applying the Hermite Wavelet Method

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Détails bibliographiques
Publié dans:	Mathematics vol. 13, no. 3 (2025), p. 528
Auteur principal:	Zhang, Yimiao
Autres auteurs:	Afridi, Muhammad Idrees, Muhammad Samad Khan, Amanullah
Publié:	MDPI AG
Sujets:	Accuracy Mathematical analysis Wavelet transforms Collocation methods Hermite polynomials Mathematical functions Approximation Numerical analysis Fourier analysis Differential equations Mathematicians Viscoelasticity Numerical methods Boundary conditions Wavelet analysis Constants Efficiency
Accès en ligne:	Citation/Abstract Full Text + Graphics Full Text - PDF
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Description
Résumé:	In this paper, we introduce the Hermite wavelet method (HWM), a numerical method for the fractional-order Bagley–Torvik equation (BTE) solution. The recommended method is based on a polynomial called the Hermite polynomial. This method uses collocation points to turn the given differential equation into an algebraic equation system. We can find the values of the unknown constants after solving the system of equations using the Maple program. The required approximation of the answer was obtained by entering the numerical values of the unknown constants. The approximate solution for the given fractional-order differential equation is also shown graphically and numerically. The suggested method yields straightforward results that closely match the precise solution. The proposed methodology is computationally efficient and produces more accurate findings than earlier numerical approaches.
ISSN:	2227-7390
DOI:	10.3390/math13030528
Source:	Engineering Database