Volume 16, Issue 3
Stability and Convergence of an Implicit Difference Approximation for the Space Riesz Fractional Reaction-Dispersion Equation

J. H. Chen & F. W. Liu

Numer. Math. J. Chinese Univ. (English Ser.), 16 (2007), pp. 253-264.

Published online: 2007-08

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  • Abstract
In this paper, we consider a Riesz space-fractional reaction-dispersion equation (RSFRDE). The RSFRDE is obtained from the classical reaction-dispersion equation by replacing the second-order space derivative with a Riesz derivative of order $\beta\in (1,2].$ We propose an implicit finite difference approximation for RSFRDE. The stability and convergence of the finite difference approximations are analyzed. Numerical results are found in good agreement with the theoretical analysis.
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@Article{NM-16-253, author = {}, title = {Stability and Convergence of an Implicit Difference Approximation for the Space Riesz Fractional Reaction-Dispersion Equation}, journal = {Numerical Mathematics, a Journal of Chinese Universities}, year = {2007}, volume = {16}, number = {3}, pages = {253--264}, abstract = {In this paper, we consider a Riesz space-fractional reaction-dispersion equation (RSFRDE). The RSFRDE is obtained from the classical reaction-dispersion equation by replacing the second-order space derivative with a Riesz derivative of order $\beta\in (1,2].$ We propose an implicit finite difference approximation for RSFRDE. The stability and convergence of the finite difference approximations are analyzed. Numerical results are found in good agreement with the theoretical analysis.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/nm/10069.html} }
TY - JOUR T1 - Stability and Convergence of an Implicit Difference Approximation for the Space Riesz Fractional Reaction-Dispersion Equation JO - Numerical Mathematics, a Journal of Chinese Universities VL - 3 SP - 253 EP - 264 PY - 2007 DA - 2007/08 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/nm/10069.html KW - AB - In this paper, we consider a Riesz space-fractional reaction-dispersion equation (RSFRDE). The RSFRDE is obtained from the classical reaction-dispersion equation by replacing the second-order space derivative with a Riesz derivative of order $\beta\in (1,2].$ We propose an implicit finite difference approximation for RSFRDE. The stability and convergence of the finite difference approximations are analyzed. Numerical results are found in good agreement with the theoretical analysis.
J. H. Chen & F. W. Liu. (2019). Stability and Convergence of an Implicit Difference Approximation for the Space Riesz Fractional Reaction-Dispersion Equation. Numerical Mathematics, a Journal of Chinese Universities. 16 (3). 253-264. doi:
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