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

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.