标题：A block-centred finite difference method for the distributed-order differential equation with Neumann boundary condition
作者：Li, Xiaoli; Rui, Hongxing
作者机构：[Li, Xiaoli; Rui, Hongxing] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China.
通讯作者：Rui, HX;Rui, Hongxing
通讯作者地址：[Rui, HX]Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China.
来源：INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
关键词：Block-centred finite difference; distributed-order differential; equation; stability; priori estimates; numerical experiments
摘要：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 convergence O(Delta t(1+sigma/2) + h(2) + k(2) + sigma(2)) both for pressure and velocity are established on non-uniform rectangular grids, where Delta t, h, k and sigma 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.