Compact Implicit Integration Factor Method for the Nonlinear Dirac Equation. (18th October 2017)

• Record Type: Journal Article
• Authors: Zhang, Jing-Jing; Li, Xiang-Gui; Shao, Jing-Fang
• Other Names: Villatoro Francisco R. Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2017(2017)
• Publication Date: 2017-10-18
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2017/3634815
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : A high-order accuracy numerical method is proposed to solve the ( 1 + 1 ) -dimensional nonlinear Dirac equation in this work. We construct the compact finite difference scheme for the spatial discretization and obtain a nonlinear ordinary differential system. For the temporal discretization, the implicit integration factor method is applied to deal with the nonlinear system. We therefore develop two implicit integration factor numerical schemes with full discretization, one of which can achieve fourth-order accuracy in both space and time. Numerical results are given to validate the accuracy of these schemes and to study the interaction dynamics of the nonlinear Dirac solitary waves.