A new numerical method for fractional diffusion equation based on Padé approximation

In this work, a fourth order L-stable method based on Padé scheme for solving fractional diffusion equation with Riesz derivative has been discussed. Second order discretization method is applied for spatial variable. First order system obtained from this discretization is solved by fourth order L-stable method. Illustrative example is included to show the accuracy and applicability of the new technique presented in the current paper.