novel second-order accurate implicit numerical methods for the riesz space distributed-order advection-dispersion equations
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ID: 163958
2015
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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.
| Reference Key |
wang2015advancesnovel
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|---|---|
| Authors | ;X. Wang;F. Liu;X. Chen |
| Journal | theater |
| Year | 2015 |
| DOI |
10.1155/2015/590435
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