Fractional centered difference scheme for high-dimensional integral fractional Laplacian

In this work we study the finite difference method for fractional diffusion equation with high-dimensional hyper-singular integral Laplacian. We first propose a simple and easy-to-implement discrete approximation, i.e., centered scheme γth-order (γ≤2) convergence operator. Based on established then construct to solve equations analyze stability in energy norm (0<α≤2) maximum (1<α≤2). further present fast solver linear system which is obtained by discretization rectangular domain use fictitious extend non-rectangular one. Several numerical results are provided support our theoretical results.