Preconditioned quasi-compact boundary value methods for space-fractional diffusion equations

This paper focuses on highly efficient numerical methods for solving space-fractional diffusion equations. By combining the fourth-order quasi-compact difference scheme and boundary value methods, a class of quasi-compact boundary value methods are constructed. In order to accelerate the convergence rate of this class of methods, the Kronecker product splitting (KPS) iteration method and the preconditioned method with KPS preconditioner are proposed. A convergence criterion for the KPS iteration method is derived. A numerical experiment further illustrates the computational efficiency and accuracy of the proposed methods. Moreover, a numerical comparison with the preconditioned method with Strang-type preconditioner is given, which shows that the preconditioned method with KPS preconditioner is comparable in computational efficiency.