A space-time spectral collocation method for the two-dimensional variable-order fractional percolation equations

In this article, we introduce a space-time spectral collocation method for solving the two-dimensional variable-order fractional percolation equations. The method is based on a Legendre-Gauss-Lobatto (LGL) spectral collocation method for discretizing spatial and the spectral collocation method for the time integration of the resulting linear first-order system of ordinary differential equation. Optimal priori error estimates in L2 norms for the semi-discrete and full-discrete formulation are derived. The method has spectral accuracy in both space and time. Numerical results confirm the exponential convergence of the proposed method in both space and time.