TY - JOUR
T1 - High Order Difference Schemes for a Time Fractional Differential Equation with Neumann Boundary Conditions
JO - East Asian Journal on Applied Mathematics
VL - 3
SP - 222
EP - 241
PY - 2018
DA - 2018/02
SN - 4
DO - http://doi.org/10.4208/eajam.281013.300414a
UR - https://global-sci.org/intro/article_detail/eajam/10834.html
KW - Time fractional differential equation, Neumann boundary conditions, compact ADI scheme, weighted and shifted Grunwald difference operator, convergence.
AB - <p style="text-align: justify;">A compact finite difference scheme is derived for a time fractional differential
equation subject to Neumann boundary conditions. The proposed scheme is second-order accurate in time and fourth-order accurate in space. In addition, a high order alternating direction implicit (ADI) scheme is also constructed for the two-dimensional case. The stability and convergence of the schemes are analysed using their matrix forms.</p>