An implicit finite difference method is developed for a one-dimensional frac- tional percolation equation （FPE） with the Dirichlet and fractional boundary conditions. The stability and convergence are discussed for ...An implicit finite difference method is developed for a one-dimensional frac- tional percolation equation （FPE） with the Dirichlet and fractional boundary conditions. The stability and convergence are discussed for two special cases, i.e., a continued seep- age flow with a monotone percolation coefficient and a seepage flow with the fractional Neumann boundary condition. The accuracy and efficiency of the method are checked with two numerical examples.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11171193 and11371229)the Natural Science Foundation of Shandong Province(No.ZR2014AM033)the Science and Technology Development Project of Shandong Province(No.2012GGB01198)
文摘An implicit finite difference method is developed for a one-dimensional frac- tional percolation equation （FPE） with the Dirichlet and fractional boundary conditions. The stability and convergence are discussed for two special cases, i.e., a continued seep- age flow with a monotone percolation coefficient and a seepage flow with the fractional Neumann boundary condition. The accuracy and efficiency of the method are checked with two numerical examples.
