Higher order compact finite difference method for the solution of 2-D time fractional diffusion equation

The main purpose of this study is to work on the solution of two-dimensional time fractional diffusion equation In this research work we apply the HOC scheme to approximate the second order space derivative. To obtain a discrete implicit scheme, Grunwald-Letnikov descritization is used in sense to approximate the Riemann-Liouville time fractional derivative. The scheme thus obtained is based on block pentadiagonal matrix and each matrix has five-point stencil in order to reduce the computational cost we use AOS method. In AOS method, before taking the average of two solutions first we split the n-dimensional problems into a sum of n-one dimensional problem.