A block‐centered finite difference method for fractional Cattaneo equation. Issue 1 (23rd August 2017) - Li, Xiaoli; Rui, Hongxing; Liu, Zhengguang
Abstract : In this article, a block‐centered finite difference method for fractional Cattaneo equation is introduced and analyzed. The unconditional stability and the global convergence of the scheme are proved rigorously. Some a priori estimates of discrete L 2 norm with optimal order of convergence O ( Δ t 3 − α + h 2 + k 2 ) both for pressure and velocity are established on nonuniform rectangular grids. Moreover, the applicability and accuracy of the scheme are demonstrated by numerical experiments to support our theoretical analysis.