High Order Difference Schemes for a Time Fractional Differential Equation with Neumann Boundary Conditions
DOI:
https://doi.org/10.4208/eajam.281013.300414aKeywords:
Time fractional differential equation, Neumann boundary conditions, compact ADI scheme, weighted and shifted Grunwald difference operator, convergence.Abstract
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.