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Discrete Dynamics in Nature and Society
Volume 2017, Article ID 3634815, 8 pages
https://doi.org/10.1155/2017/3634815
Research Article

Compact Implicit Integration Factor Method for the Nonlinear Dirac Equation

School of Applied Sciences, Beijing Information Science and Technology University, Beijing 100192, China

Correspondence should be addressed to Jing-Jing Zhang; moc.361@2111gnahzgnijgnij

Received 18 June 2017; Revised 7 September 2017; Accepted 19 September 2017; Published 18 October 2017

Academic Editor: Francisco R. Villatoro

Copyright © 2017 Jing-Jing Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A high-order accuracy numerical method is proposed to solve the -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.