| Abstract: | 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 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. |
