An efficient GL-ADI general finite difference method for three dimensional nonlocal diffusion equations with anisotropic diffusion coefficients

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Abstract

This paper is concerned with an alternating direction implicit (ADI) general finite difference method (GFDM) for solving three-dimensional nonlocal diffusion equations with anisotropic diffusion coefficients. The Grünwald-Letnikov (GL) approximation is adopted to discretize the Caputo fractional derivatives on uniform grids. This spatial direction is handled by using the general difference method. A fully discrete GL-ADI general difference scheme is strictly constructed. The existence, uniqueness, stability, and convergence of numerical solution are proved. In addition, numerical experiments are carried out to confirm the validity of the theoretical analysis.

Keywords

nonlocal diffusion equation / ADI method / Grünwald-Letnikov scheme / finite difference method / stability and convergence

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