Analysis and numerical methods for the Riesz space distributed-order advection-diffusion equation with time delay
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Mohammad Javidi [1] ; Mahdi Saedshoar Heris [1]
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[1] La Universidad de Tabriz
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- Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol. 76, Nº. 4, 2019, págs. 533-551
- Idioma: inglés
- DOI: 10.1007/s40324-019-00192-z
- Texto completo no disponible (Saber más ...)
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Resumen
In this paper, we investigate the fractional backward differential formulas (FBDF) and Grünwald difference method for the Riesz space distributed-order advection-diffusion equation with delay. The midpoint quadrature rule is used to approximate the distributed-order equation by a multi-term fractional form. Next the transformed multi-term fractional equation is solved by discretizing in space by the fractional backward differential formulas method for 0<α<1 and the shifted Grünwald difference operators for 1<β<2 to approximate the Riesz space fractional derivative and in time by using the Crank-Nicolson scheme. We prove that the Crank-Nicolson scheme is conditionally stable and convergent with second-order accuracy O(h2+κ2+σ2+ρ2). Finally, we give some examples and compare the results of our method with two works. This results show the effectiveness of the proposed numerical method.
