A block‐centered finite difference method for fractional Cattaneo equation. Issue 1 (23rd August 2017)

• Record Type: Journal Article
• Authors: Li, Xiaoli; Rui, Hongxing; Liu, Zhengguang
• Is Part Of: Numerical methods for partial differential equations. Volume 34:Issue 1(2018)
• Page Start: 296
• Page End: 316
• Publication Date: 2017-08-23
• Subjects: block‐centered finite difference -- fractional Cattaneo equation -- nonuniform rectangular grids -- numerical experiments; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22198
• Languages: English
• ISSNs: 0749-159X

Abstract

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.