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  

MODIFIED ALTERNATING DIRECTION METHODS FOR SOLVING A TWO-DIMENSIONAL NON-CONTINUOUS SEEPAGE FLOW WITH FRACTIONAL DERIVATIVES

作　　者：刘青霞[1] 刘发旺[2] 

机构地区：[1]厦门大学数学科学学院,福建厦门361005 [2]澳大利亚昆士兰理工大学数学科学学院

出　　处：《计算数学》2009年第2期179-194,共16页Mathematica Numerica Sinica

基　　金：国家自然科学基金(10271098)资助项目.

摘　　要：本文考虑在二维均匀介质中带有分数阶导数的非连续渗流问题,此模型修正了众所周知的Darcy原理.利用Riemann-Liouville和Grünwald-Letnikov分数阶导数之间的关系,提出了求解在二维均匀介质中带有分数阶导数的非连续渗流问题的两种修正的交替方向法:修正的交替方向隐式Euler方法和修正的Peaceman-Rachford方法.我们讨论了这两种方法的稳定性,相容性和收敛性.最后给出数值例子.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 Grunwald-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.

关 键 词：非连续渗流 交替方向方法 分数阶导数 稳定性 收敛性 

分 类 号：O357.3[理学—流体力学]