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- Title
Compact Implicit Integration Factor Method for the Nonlinear Dirac Equation.
- Authors
Zhang, Jing-Jing; Li, Xiang-Gui; Shao, Jing-Fang
- 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.
- Subjects
DIRAC equation; NUMERICAL analysis; PARTIAL differential equations; SPATIAL distribution (Quantum optics); EXTERIOR differential systems
- Publication
Discrete Dynamics in Nature & Society, 2017, p1
- ISSN
1026-0226
- Publication type
Article
- DOI
10.1155/2017/3634815