Novel Second‐Order Accurate Implicit Numerical Methods for the Riesz Space Distributed‐Order Advection‐Dispersion Equations

X. Wang, F. Liu and X. Chen

Advances in Mathematical Physics, 2015, vol. 2015, issue 1

Abstract: We derive and analyze second‐order accurate implicit numerical methods for the Riesz space distributed‐order advection‐dispersion equations (RSDO‐ADE) in one‐dimensional (1D) and two‐dimensional (2D) cases, respectively. Firstly, we discretize the Riesz space distributed‐order advection‐dispersion equations into multiterm Riesz space fractional advection‐dispersion equations (MT‐RSDO‐ADE) by using the midpoint quadrature rule. Secondly, we propose a second‐order accurate implicit numerical method for the MT‐RSDO‐ADE. Thirdly, stability and convergence are discussed. We investigate the numerical solution and analysis of the RSDO‐ADE in 1D case. Then we discuss the RSDO‐ADE in 2D case. For 2D case, we propose a new second‐order accurate implicit alternating direction method, and the stability and convergence of this method are proved. Finally, numerical results are presented to support our theoretical analysis.

Date: 2015
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https://doi.org/10.1155/2015/590435

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2015:y:2015:i:1:n:590435

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