High order difference schemes for a time fractional differential equation with Neumann boundary conditions

摘要

Based on our recent results, in this paper, a compact finite differencescheme is derived for a time fractional differential equation subject to theNeumann boundary conditions. The proposed scheme is second order accurate intime and fourth order accurate in space. In addition, a high order alternatingdirection implicit (ADI) scheme is also constructed for the two-dimensionalcase. Stability and convergence of the schemes are analyzed using their matrixforms.