Operational matrix based numerical scheme for the solution of time fractional diffusion equations

This paper presents a numerical method based on an operational matrix of Legendre polynomials for resolving the class of time fractional diffusion (TFD) equations. The operational matrix of fractional order derivatives of the Legendre polynomials is derived as a product of matrices. The collocation method together with the operational matrix of Legendre polynomials are employed to transform the TFD equations into a set of algebraic equations. The perturbation method is applied to show the stability of the discussed method. The accuracy of the suggested method is validated using numerical experiments. The solution obtained by this method is in excellent agreement with the exact solution for the integer order of derivatives and is more precise than the solution obtained by the existing method in which Bernstein polynomials are taken as the basis polynomials.