TY - JOUR
T1 - High Accuracy Spectral Method for the Space-Fractional Diffusion Equations
AU - Zhai , Shuying
AU - Gui , Dongwei
AU - Zhao , Jianping
AU - Feng , Xinlong
JO - Journal of Mathematical Study
VL - 3
SP - 274
EP - 286
PY - 2014
DA - 2014/09
SN - 47
DO - http://doi.org/10.4208/jms.v47n3.14.03
UR - https://global-sci.org/intro/article_detail/jms/9958.html
KW - Space-fractional diffusion equation, fractional Laplacian, Chebyshev collocation method, Fourier spectral method, implicit-explicit Runge-Kutta method.
AB - <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>