Numerical Solution of Fractional Diffusion Equation by Shifted Legendre Operational Matrix Method and Fractional Linear Multi-step Methods

The paper deals with an efficient scheme to solve fractional diffusion equation including both time and spatial fractional derivative in Caputo sense. In the first time, the so-called operational matrice was obtained by computating fractional derivative of shifted Legendre polynomial followed by applying the spectral Tau method that convert the original equation in the system of fractionnal ordinary differential equation (FODE). The fractionnal linear multi-step metthods (FLMMS) can be used in the second time to give the approximate solution. To acces the accuracy and validity of the method, two illustratives examples are reported using Matlab code.