Higher order compact finite difference method for the solution of 2-D time fractional diffusion equation
Journal: Matrix Science Mathematic (MSMK)
Author: Muhammad Usman, Noor Badshah, Fazal Ghaffar
This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
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.