@Article{EAJAM-14-1,
author = {Ying, He and Yan, Wang and Zhijian, Yang, Jerry and Yin, Hongshuang},
title = {Numerical Methods for the Nonlinear Dirac Equation in the Massless Nonrelativistic Regime},
journal = {East Asian Journal on Applied Mathematics},
year = {2024},
volume = {14},
number = {1},
pages = {79--103},
abstract = {<p style="text-align: justify;">Numerical methods for the nonlinear Dirac equation (NDE) in the massless
nonrelativistic regime are considered. In this regime, the equation contains a small dimensionless parameter $0 &lt;\varepsilon≤ 1,$ and its solution is highly oscillatory in time. We
present and analyze traditional numerical schemes for the NDE, including finite difference methods, time-splitting methods and exponential integrators. Error analysis indicates that all these methods require an $\varepsilon$-dependent time-step size to achieve an optimal
convergence order. Utilizing an operator splitting technique, we propose a uniformly accurate (UA) scheme. The scheme enables first-order convergence in time for all $\varepsilon ∈ (0, 1]$ without restrictions on time-step size. Error estimates for the UA scheme are rigorously
established and numerical results confirm the properties of the method.</p>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.2023-004.200423},
url = {https://global-sci.com/article/82399/numerical-methods-for-the-nonlinear-dirac-equation-in-the-massless-nonrelativistic-regime}
}