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arXiv · 1811.10513

Second order difference approximation for a class of Riesz space fractional advection-dispersion equations with delay

M. Saedshoar Heris·M. Javidi
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Abstract

In this paper, we propose numerical scheme for the Riesz space fractional advection-dispersion equations with delay (RFADED). Firstly, analytical solution for RFADED in terms of the functions of Mittag-Leffler type is derived. Secondly, the fractional backward differential formulas (FBDF) method and shifted Grünwald method are introduced to the Riesz space fractional derivatives. Next, stability and convergency of these methods have been proved. Thirdly, Crank-Nicolson scheme for solving this problem is proposed. We prove that the scheme is conditionally stable and convergent with the order accuracy of ${\rm O}({κ^2} + {h^2})$. Finally, some numerical results are given to demonstrate that presented method is a computationally efficient and accurate method for solving RFADED.

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M. Saedshoar Heris, M. Javidi. 2021-07-21. Second order difference approximation for a class of Riesz space fractional advection-dispersion equations with delay. https://arxiv.org/abs/1811.10513

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