Stability and convergence based on the finite difference method for the nonlinear fractional cable equation on non-uniform staggered grids

摘要

In this article, a block-centered finite difference method for the nonlinear fractional cable equation is introduced and analyzed. The unconditional stability and the global convergence of the scheme are proved rigorously. Some a priori estimates of discrete norms with optimal order of convergence O(Δt~α + h~2 + k~2) both for pressure and velocity are established on non-uniform rectangular grids, where α = min{1 + γ_1, 1 + γ_2}. Δt, h and k are the step sizes in time, space in x- and y-direction. Moreover, the applicability and accuracy of the scheme are demonstrated by numerical experiments to support our theoretical analysis.