Fourth Order Difference Approximations for Space Riemann-Liouville Derivatives Based on Weighted and Shifted Lubich Difference Operators  

作　　者：Minghua Chen Weihua Deng 

机构地区：[1]School of Mathematics and Statistics,Lanzhou University,Lanzhou 730000,P.R.China.

出　　处：《Communications in Computational Physics》2014年第7期516-540,共25页计算物理通讯（英文）

基　　金：supported by the National Natural Science Foundation of China under Grant No.11271173,the Fundamental Research Funds for the Central Universities under Grant No.lzujbky-2014-228,and the Program for New Century Excellent Talents in University under Grant No.NCET-09-0438.

摘　　要：High order discretization schemes playmore 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 with first order schemes but the accuracy is greatly improved.Using the fractional linear multistep methods,Lubich obtains the n-th order(n≤6)approximations of the a-th derivative(a>0)or integral(a<0)[Lubich,SIAM J.Math.Anal.,17,704-719,1986],because of the stability issue the obtained scheme can not be directly applied to the space fractional operator with a∈(1,2)for time dependent problem.By weighting and shifting Lubich’s 2nd order discretization scheme,in[Chen&Deng,SINUM,arXiv:1304.7425]we derive a series of effective high order discretizations for space fractional derivative,called WSLD operators there.As the sequel of the previous work,we further provide new high order schemes for space fractional derivatives by weighting and shifting Lubich’s 3rd and 4th order discretizations.In particular,we prove that the obtained 4th order approximations are effective for space fractional derivatives.And the corresponding schemes are used to solve the space fractional diffusion equation with variable coefficients.

关 键 词：Fractional derivatives high order scheme weighted and shifted Lubich difference(WSLD)operators numerical stability 

分 类 号：O17[理学—数学]