Compact Implicit Integration Factor Method for the Nonlinear Dirac Equation

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...

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Bibliographic Details
Published inDiscrete dynamics in nature and society Vol. 2017; no. 2017; pp. 1 - 8
Main Authors Zhang, Jing-Jing, Shao, Jing-Fang, Li, Xiang-Gui
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Publishing Corporation 01.01.2017
Hindawi
John Wiley & Sons, Inc
Hindawi Limited
Wiley
Subjects
Accuracy
Applied mathematics
Boundary conditions
Boundary layer
Computational physics
Dimensional analysis
Dirac equation
Discretization
Finite difference method
Mathematical research
Methods
Nonlinear systems
Numerical analysis
Partial differential equations
Relativism
Solitary waves
Studies
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Summary: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.
ISSN:1026-0226
1607-887X
DOI:10.1155/2017/3634815