Numerical comparison of methods for solving spacetime fractional diffusion equation

One of the ongoing issues with fractional-order diffusion models is the design of efficient numerical schemes for the space and time discretizations. In this paper, we compare 4 different numerical discretizations of the space-time fractional diffusion model. These consist of the finite difference (FD), finite element (FE), pseudo-spectral (PS) and radial basis functions (RBFs) methods. We suggest that non-local methods, like the pseudo-spectral and radial basis functions method, are well-suited to discretize the non-local operators like fractional-order derivatives. These methods naturally take the global behavior of the solution into account and thus do not result in an extra computational cost when moving from an integer-order to a fractional-order diffusion model

کلیدواژه ها:

Space-time fractional diffusion equation ، finite difference ، finite element ، pseudo-spectral and radial basis functions method