Preconditioned Iterative Methods For Solving A Fractional Advection-Diffusion Equation

Abstract

In this paper, we consider numerical solutions of a fractional
advection-diusion equation. We rst, propose an implicit method based
on Grunwald formulae and then discuss its stability and consistency. To
improve the implicit method, we use a preconditioned generalized mini-
mal residual (PGMRES) method and preconditioned conjugate gradient
normal residual (PCGNR) method. Numerical experiments are given to
illustrate eciency of the method.
Keywords: Fractional diusion equations, Preconditioner, Conjugate gra-
dient normal residual of the method, Generalized minimal residual method.