Fourth Order Difference Approximations for Space Riemann-Liouville Derivatives Based on Weighted and Shifted Lubich Difference Operators (Communications in Computational Physics, 2014)
High order discretization schemes play more important role in fractional operatorsthan classical ones. This is because usually for classical derivatives the stencilfor high order discretization schemes is wider than low order ones; but for fractionaloperators the stencils for high order schemes and low order ones are the same. Thenusing high order schemes to solve fractional equations leads to almost the same computationalcost as first order schemes but the accuracy is greatly improved. Usingthe fractional linear multistep methods, Lubich obtains the ν-th order (ν≤6) approximationsof the α-th derivative (α>0) or integral (α