Implicit finite difference method for fractional percolation equation with Dirichlet and fractional boundary conditions

Abstract

An implicit finite difference method is developed for a one-dimensional fractional percolation equation (FPE) with the Dirichlet and fractional boundary conditions. The stability and convergence are discussed for two special cases, i.e., a continued seepage 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.