%0 Journal Article
%T MODIFIED ALTERNATING DIRECTION METHODS FOR SOLVING A TWO-DIMENSIONAL NON-CONTINUOUS SEEPAGE FLOW WITH FRACTIONAL DERIVATIVES<br>修正交替方向法求解具有分数阶导数的二维非连续渗流问题
%A Liu Qingxia
%A Liu Fawang
%A <br>刘青霞
%A 刘发旺
%J 计算数学
%D 2009
%I 
%X In this paper, a two-dimensional non-continuous seepage flow with fractional derivatives (2D-NCSF-FD) in uniform media is considered, which has modified the well-known Darcy law. Using the relationship between Riemann-Liouville and Grünwald-Letnikov fractional derivatives, two modified alternating direction methods: a modified alternating direction implicit Euler method and a modified Peaceman-Rachford method, are proposed for solving the 2D-NCSF-FD in uniform media. The stability and consistency, thus convergence of the two methods in a bounded domain are discussed. Finally, numerical results are given.
%K non-continuous seepage flow
%K alternating direction method
%K fractional derivative
%K stability
%K convergence<br>非连续渗流
%K 交替方向方法
%K 分数阶导数
%K 稳定性
%K 收敛性
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=CC77F3CEF526D9CF0B3021650FB4E57E&aid=824A4ADE774466C0158681E408F68C46&yid=DE12191FBD62783C&vid=4AD960B5AD2D111A&iid=0B39A22176CE99FB&sid=E114CF9BB47B65BE&eid=5D9D6A8FC2C66FD8&journal_id=0254-7791&journal_name=计算数学&referenced_num=0&reference_num=20