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

摘要

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 L-2 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. (C) 2018 Elsevier Ltd. All rights reserved.