The hybrid of θ−Method and spatial extrapolation for solving Fractional Diffusion Differential Equation

In this paper we examine θ− method for solving fractional diffusion differential equations for (0 ≤ θ ≤ 1). Also we use spatial extrapolation for improving results. We propose Riemann-Liouville derivative based on shifted Grunwald estimates for fractional derivative. Finally, consistency , stability and convergence analysis of the method is discussed. A numerical example is presented and compared with the exact analytical solution.

Fractional PDE (FPDE); finite differences θ− method; Riemann-Liouville derivative; shifted Grunwald formula.