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

doi:10.1007/s10483-016-2036-6

Abstract

Abstract:

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.

Key words: finite difference method, frac-tional boundary condition, stability and convergence, Riemann-Liouville derivative, fractional percolation equation (FPE), Toeplitz matrix

2010 MSC Number:

Boling GUO, Qiang XU, Zhe YIN. Implicit finite difference method for fractional percolation equation with Dirichlet and fractional boundary conditions. Applied Mathematics and Mechanics (English Edition), 2016, 37(3): 403-416.

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