TY - JOUR
T1 - A Fourth Order Finite Difference Method for Time-Space Fractional Diffusion Equations
JO - East Asian Journal on Applied Mathematics
VL - 4
SP - 764
EP - 781
PY - 2018
DA - 2018/10
SN - 8
DO - http://doi.org/10.4208/eajam.280218.210518
UR - https://global-sci.org/intro/article_detail/eajam/12818.html
KW - Fractional diffusion equation, Riesz derivative, high-order approximation, stability, convergence.
AB - <p style="text-align: justify;">A finite difference method for a class of time-space fractional diffusion equations
is considered. The trapezoidal formula and a fourth-order fractional compact difference
scheme are, respectively, used in temporal and spatial discretisations and the
method stability is studied. Theoretical estimates of the convergence in the $L_2$ -norm
are shown to be $\mathscr{O}(τ^2+h^4)$, where $τ$ and $h$ are time and space mesh sizes. Numerical
examples confirm theoretical results.</p>