Stability and convergence of compact finite difference method for parabolic problems with delay

Fengyan Wu, Dongfang Li, Jinming Wen and Jinqiao Duan

Applied Mathematics and Computation, 2018, vol. 322, issue C, 129-139

Abstract: The compact finite difference method becomes more acceptable to approximate the diffusion operator than the central finite difference method since it gives a better convergence result in spatial direction without increasing the computational cost. In this paper, we apply the compact finite difference method and the linear θ-method to numerically solve a class of parabolic problems with delay. Stability of the fully discrete numerical scheme is investigated by using the spectral radius condition. When θ∈[0,12), a sufficient and necessary condition is presented to show that the fully discrete numerical scheme is stable. When θ∈[12,1], the fully discrete numerical method is proved to be unconditionally asymptotically stable. Moreover, convergence of the fully discrete scheme is studied. Finally, several numerical examples are presented to illustrate our theoretical results.

Keywords: Parabolic problems with delay; Compact finite difference method; Asymptotic stability; Convergence (search for similar items in EconPapers)
Date: 2018
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300317308147
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:322:y:2018:i:c:p:129-139

DOI: 10.1016/j.amc.2017.11.032

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().