On Approximate Solutions for Time-Fractional Diffusion Equation

In the last decades differential equations involving fractional derivatives and integrals have been studied by many researchers. Due to their ability to model more adequately some phenomena, fractional partial differential equations have been used in numerous areas such as finance, hydrology, porous media, engineering and control systems, etc. Numerical schemes based on rotated finite difference approximation have been proven to work well in solving standard diffusion equations. However, the formulation of these strategies on time fractional diffusion counterpart is still at its infancy. A well-designed preconditioning for these types of problems reduces the number of iterations to reach convergence. In this research work, we have derived new preconditioned fractional rotated finite difference method for solving 2D time-fractional diffusion equation. Numerical experiments are conducted to examine the effectiveness of the proposed method.