@Article{AAMM-9-282,
author = {Li , Can and Deng , Weihua},
title = {A New Family of Difference Schemes for Space Fractional Advection Diffusion Equation},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2018},
volume = {9},
number = {2},
pages = {282--306},
abstract = {<p style="text-align: justify;">The second order weighted and shifted Grünwald difference (WSGD) operators
are developed in [Tian, Zhou and Deng, Math. Comput., 84 (2015), pp. 1703–1727] to solve space fractional partial differential equations. Along this direction, we
further design a new family of second order WSGD operators; by properly choosing
the weighted parameters, they can be effectively used to discretize space (Riemann-Liouville)
fractional derivatives. Based on the new second order WSGD operators,
we derive a family of difference schemes for the space fractional advection diffusion
equation. By von Neumann stability analysis, it is proved that the obtained schemes
are unconditionally stable. Finally, extensive numerical experiments are performed to
demonstrate the performance of the schemes and confirm the convergence orders.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.2015.m1069},
url = {http://global-sci.org/intro/article_detail/aamm/12149.html}
}