@Article{JMS-47-3,
author = {Zhai, Shuying and Gui, Dongwei and Zhao, Jianping and Xinlong, Feng},
title = {High Accuracy Spectral Method for the Space-Fractional Diffusion Equations},
journal = {Journal of Mathematical Study},
year = {2014},
volume = {47},
number = {3},
pages = {274--286},
abstract = {<p style="text-align: justify;">In this paper, a high order accurate spectral method is presented
for the space-fractional diffusion equations. Based on Fourier
spectral method in space and &nbsp;Chebyshev collocation method in time,
three high order accuracy schemes are proposed. The main advantages
of this method are that it yields a fully diagonal representation of
the fractional operator, with increased accuracy and efficiency
compared with low-order counterparts, and a completely
straightforward extension to high spatial dimensions. Some numerical
examples, including Allen-Cahn equation, are conducted to verify the
effectiveness of this method.</p>},
issn = {2617-8702},
doi = {https://doi.org/10.4208/jms.v47n3.14.03},
url = {https://global-sci.com/article/87852/high-accuracy-spectral-method-for-the-space-fractional-diffusion-equations}
}