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 differ- ence 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 precondi- tioned 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 numer- ical comparison with the preconditioned method with Strang-type preconditioner is given, which shows that the preconditioned method with KPS preconditioner is com- parable in computational efficiency.