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The Journal of Supercomputing
Published in:

18-04-2024

Finite difference method for the Riesz space distributed-order advection–diffusion equation with delay in 2D: convergence and stability

Authors: Mahdi Saedshoar Heris, Mohammad Javidi

Published in: The Journal of Supercomputing | Issue 12/2024

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Abstract

In this paper, we propose numerical methods for the Riesz space distributed-order advection–diffusion equation with delay in 2D. We utilize the fractional backward differential formula method of second order (FBDF2), and weighted and shifted Grünwald difference (WSGD) operators to approximate the Riesz fractional derivative and develop the finite difference method for the RFADED. It has been shown that the obtained schemes are unconditionally stable and convergent with the accuracy of \(\textrm{O}({h^2} + {k^2} +{\kappa ^2} + {\sigma ^2} + {\rho ^2})\), where h, k and \(\kappa\) are space step for x, y and time step, respectively. Also, numerical examples are constructed to demonstrate the effectiveness of the numerical methods, and the results are found to be in excellent agreement with analytic exact solution.
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Metadata
Title
Finite difference method for the Riesz space distributed-order advection–diffusion equation with delay in 2D: convergence and stability
Authors
Mahdi Saedshoar Heris
Mohammad Javidi
Publication date
18-04-2024
Publisher
Springer US
Published in
The Journal of Supercomputing / Issue 12/2024
Print ISSN: 0920-8542
Electronic ISSN: 1573-0484
DOI
https://doi.org/10.1007/s11227-024-06112-x

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