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Efficient polynomial kernel-based method for multi-term time-fractional diffusion systems in regular and irregular domains.

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Titel: Efficient polynomial kernel-based method for multi-term time-fractional diffusion systems in regular and irregular domains.
Autoren: Azarnavid, Babak1 (AUTHOR) babakazarnavid@ubonab.ac.ir, Fardi, Mojtaba2 (AUTHOR) m.fardi@sku.ac.ir, Emami, Hojjat1,3 (AUTHOR) emami@ubonab.ac.ir
Quelle: Chaos, Solitons & Fractals. Oct2025:Part 1, Vol. 199, pN.PAG-N.PAG. 1p.
Schlagwörter: *BERNOULLI polynomials, *POLYNOMIAL approximation, *HEAT equation, *POLYNOMIALS, *COMPUTER simulation
Abstract: This paper presents an efficient polynomial kernel-based method for solving multi-term nonlinear time-fractional diffusion systems in high-dimensional regular and irregular domains. Time-fractional diffusion equations are increasingly recognized for their ability to model complex phenomena across various disciplines, including physics, engineering, and finance. By incorporating fractional-order temporal derivatives, these equations effectively capture nonlocal memory effects and intricate dynamics in the studied systems. We aim to provide an effective method for obtaining suitable approximate solutions to the time-fractional diffusion system of equations, which presents a significant challenge in numerical methods. We utilized the properties of Bernoulli polynomials to construct approximations in a finite-dimensional reproducing kernel space. The time-fractional system of equations is discretized using a polynomial kernel-based technique in the spatial direction. Then, an accurate high-order backward differentiation formula is utilized for time discretization. A thorough convergence analysis is conducted, establishing error bounds for the proposed method. To validate the versatility and effectiveness of the method, we conduct several numerical simulations demonstrating its performance across two and three dimensional domains. • A polynomial kernel method for solving nonlinear time-fractional diffusion systems • Using a kernel-based pseudo-spectral method for regular and irregular domains • Applying the Lubich convolution quadrature to handle fractional-order integrals • A rigorous convergence analysis and establishing error bounds • Extensive numerical simulations in both two and three-dimensional domains [ABSTRACT FROM AUTHOR]
Datenbank: Academic Search Index
Beschreibung
Abstract:This paper presents an efficient polynomial kernel-based method for solving multi-term nonlinear time-fractional diffusion systems in high-dimensional regular and irregular domains. Time-fractional diffusion equations are increasingly recognized for their ability to model complex phenomena across various disciplines, including physics, engineering, and finance. By incorporating fractional-order temporal derivatives, these equations effectively capture nonlocal memory effects and intricate dynamics in the studied systems. We aim to provide an effective method for obtaining suitable approximate solutions to the time-fractional diffusion system of equations, which presents a significant challenge in numerical methods. We utilized the properties of Bernoulli polynomials to construct approximations in a finite-dimensional reproducing kernel space. The time-fractional system of equations is discretized using a polynomial kernel-based technique in the spatial direction. Then, an accurate high-order backward differentiation formula is utilized for time discretization. A thorough convergence analysis is conducted, establishing error bounds for the proposed method. To validate the versatility and effectiveness of the method, we conduct several numerical simulations demonstrating its performance across two and three dimensional domains. • A polynomial kernel method for solving nonlinear time-fractional diffusion systems • Using a kernel-based pseudo-spectral method for regular and irregular domains • Applying the Lubich convolution quadrature to handle fractional-order integrals • A rigorous convergence analysis and establishing error bounds • Extensive numerical simulations in both two and three-dimensional domains [ABSTRACT FROM AUTHOR]
ISSN:09600779
DOI:10.1016/j.chaos.2025.116666