Title A new numerical method for fractional diffusion equation based on Pade approximation Type of Research Presentation Keywords Finite difference method, Pade scheme, L-stable method, fractional diffusion equation Abstract In this work a fourth order L-stable method based on Pade 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 discretion 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. Researchers Hamideh ghafori (First Researcher)، Ali Khani (Second Researcher)، Mojtaba Ranjbar (Third Researcher)