New approach for solving fractional diffusion wave propagation using spectral methods

This paper is concerned with the numerical solutions of a two-dimensional space-time differential equation used to model the dynamic properties of complex systems governed by diffusion. To implement the new method, we use the Legendre polynomials to approximate the unknown function. Our numerical method is based upon Ritz spectral method in which have a good pliability to meet initial and boundary conditions of the problem. We also discuss on the convergence of the new scheme. At last, an example with numerical simulations is included to show the analytical achievements numerically.