Computational spectral method for solving two-dimensional Riesz multi-term time-fractional diffusion equation

This research introduces a spectral element method (SEM) for solving a fractional diffusion model. We propose a discrete-time scheme, using the finite difference method to approach the multi-Caputo fractional derivative on a uniform mesh. In addition, we offer a Galerkin variational formulation to establish the unconditional stability of the scheme. We use the SEM based on Legendre polynomials in the space direction and derive the fully discrete scheme. The error estimation analysis of the fully discrete scheme is proved in the L2 sense. Finally, we demonstrate the method’s effectiveness by numerical experiments and simulations performed in MATLAB.