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Discrete Dynamics in Nature and Society
Volume 2016 (2016), Article ID 3670139, 8 pages
http://dx.doi.org/10.1155/2016/3670139
Research Article

Time-Compact Scheme for the One-Dimensional Dirac Equation

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

Received 26 July 2016; Accepted 4 September 2016

Academic Editor: Cengiz Çinar

Copyright © 2016 Jun-Jie Cao 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

Based on the Lie-algebra, a new time-compact scheme is proposed to solve the one-dimensional Dirac equation. This time-compact scheme is proved to satisfy the conservation of discrete charge and is unconditionally stable. The time-compact scheme is of fourth-order accuracy in time and spectral order accuracy in space. Numerical examples are given to test our results.