A finite difference scheme on graded meshes for time-fractional nonlinear Korteweg-de Vries equation

Jinye Shen, Zhi-zhong Sun and Wanrong Cao

Applied Mathematics and Computation, 2019, vol. 361, issue C, 752-765

Abstract: In this paper, a finite difference scheme for time-fractional nonlinear Korteweg-de Vries (KdV) problems with the Caputo-type fractional derivative is presented. To deal with the weak singularity caused by the fractional derivative that the solution has in the initial layer, the well-known L1 scheme on graded meshes has been used for time discretization. Meanwhile, a nonlinear finite difference approximation on uniform meshes is proposed for spatial discretization. The existence, stability and convergence of the numerical solution are studied by the energy method. It is proved that the scheme is of min{2−α,rα} order convergence in time and of first-order convergence in space, where α is the order of fractional derivative and r is a parameter of graded meshes. Furthermore, in order to increase computational efficiency, the corresponding fast algorithm of the presented scheme has been considered. In numerical simulation, a valid approach based on linear interpolation is designed to test convergence rate for the scheme on temporal graded meshes. Numerical results demonstrate sharpness of the theoretical convergence estimate and effectiveness of the fast algorithm.

Keywords: Nonlinear KdV equation; The energy method; Nonsmooth solution; Stability; Convergence order (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300319304886
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:361:y:2019:i:c:p:752-765

DOI: 10.1016/j.amc.2019.06.023

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 ().