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

Gorde:
Argitaratua izan da:Mathematics vol. 13, no. 3 (2025), p. 528
Egile nagusia: Zhang, Yimiao
Beste egile batzuk: Afridi, Muhammad Idrees, Muhammad Samad Khan, Amanullah
Argitaratua:
MDPI AG
Gaiak:
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
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Laburpena: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
Baliabidea:Engineering Database