A block-centred finite difference method for the distributed-order differential equation with Neumann boundary condition. Issue 3 (4th March 2019)

• Record Type: Journal Article
• Authors: Li, Xiaoli; Rui, Hongxing
• Is Part Of: International journal of computer mathematics. Volume 96:Issue 3(2019)
• Page Start: 622
• Page End: 639
• Publication Date: 2019-03-04
• Subjects: Block-centred finite difference -- distributed-order differential equation -- stability -- priori estimates -- numerical experiments; 65M06 -- 65M12 -- 65M15 -- 26A33; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2018.1455093
• Languages: English
• ISSNs: 0020-7160

Abstract

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.