TY - JOUR
T1 - Uniformly Stable Explicitly Solvable Finite Difference Method for Fractional Diffusion Equations
AU - Hongxing Rui & Jian Huang
JO - East Asian Journal on Applied Mathematics
VL - 1
SP - 29
EP - 47
PY - 2018
DA - 2018/02
SN - 5
DO - http://doi.org/10.4208/eajam.030614.051114a
UR - https://global-sci.org/intro/article_detail/eajam/10776.html
KW - Finite difference scheme, fractional diffusion equation, uniformly stable, explicitly solvable method, asymmetric technique, error estimate.
AB - <p style="text-align: justify;">A finite difference scheme for the one-dimensional space fractional diffusion
equation is presented and analysed. The scheme is constructed by modifying the shifted
Grünwald approximation to the spatial fractional derivative and using an asymmetric
discretisation technique. By calculating the unknowns in differential nodal point sequences
at the odd and even time levels, the discrete solution of the scheme can be
obtained explicitly. We prove that the scheme is uniformly stable. The error between
the discrete solution and the analytical solution in the discrete $l^2$ norm is optimal in
some cases. Numerical results for several examples are consistent with the theoretical
analysis.</p>