General linear and spectral Galerkin methods for the Riesz space fractional diffusion equation

Abstract The general linear method is considered to discretize the temporal term of Riesz space fractional diffusion equation. Combined with a spectral Galerkin method in the spatial direction, a method with high global accuracy is constructed. If the general linear method is algebraically stable, the stability is proven for the full discretization. Furthermore, under some conditions, the convergence order in time and the optimal error estimate in space are also obtained. Meanwhile, numerical examples are given to confirm the theoretical results.