A block-centred finite difference method for the distributed-order differential equation with Neumann boundary condition. Issue 3 (4th March 2019) - Li, Xiaoli; Rui, Hongxing
ABSTRACT: In this article, a block-centred finite difference method for the distributed-order differential equation with Neumann boundary condition is introduced and analysed. The stability and the global convergence of the scheme are proved rigorously. Some a priori estimates of discrete norms with optimal order of convergenceO ( Δ t 1 + σ / 2 + h 2 + k 2 + σ 2 ) both for pressure and velocity are established on non-uniform rectangular grids, whereΔ t, h, k and σ are the step sizes in time, space in x - and y -direction, and distributed order. Moreover, the applicability and accuracy of the scheme are demonstrated by numerical experiments to support our theoretical analysis.