(untitled) (Communications in Computational Physics, 2014)
High order discretization schemes play more important role in fractional operators than classical ones. This is because usually for classical derivatives the stencil for high order discretization schemes is wider than low order ones; but for fractional operators the stencils for high order schemes and low order ones are the same. Then using high order schemes to solve fractional equations leads to almost the same computational cost as first order schemes but the accuracy is greatly improved. Using the fractional linear multistep methods, Lubich obtains the ν-th order (ν≤6) approximations of the α-th derivative (α>0) or integral (α