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, 1-14

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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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlamp:590435

DOI: 10.1155/2015/590435

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