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The peridynamic differential operator for solving time-fractional partial differential equations

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Abstract

In this paper, the numerical solution of time-fractional convection diffusion equations (TF-CDEs) is considered as a generalization of classical ones, nonexponential relaxation patterns and anomalous diffusion. A nonlocal model further is developed toward such problems via peridynamic differential operator, which may be utilized to derive all partial derivatives of higher orders concurrently in a simple and effective manner, with no need for shape functions. To generate the final discrete system of equations, only functionals based on nonlocal operators are required, greatly simplifying the implementation. The main contribution of this work is three-fold: (1) a finite difference/nonlocal operator method is contracted for the discretization of the TF-CDEs; (2) a detailed analysis of the proposed scheme is given by providing some stability and error estimates, and the method convergence is established; and eventually, (3) numerical experiments are presented to substantiate the theoretical analysis and demonstrate the computational efficiency of the schemes.

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  1. Institute for Advanced Study, Nanchang University, Nanchang, 330031, China

    Vahid Reza Hosseini & Wennan Zou

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  1. Vahid Reza Hosseini
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Correspondence to Vahid Reza Hosseini.

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Hosseini, V.R., Zou, W. The peridynamic differential operator for solving time-fractional partial differential equations. Nonlinear Dyn 109, 1823–1850 (2022). https://doi.org/10.1007/s11071-022-07424-4

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