Abstract
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(Δtα+h2+k2) both for pressure and velocity are established on non-uniform rectangular grids, where α=min{1+γ1,1+γ2}, 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.
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