# Uniformly accurate numerical schemes for the nonlinear Dirac equation in the nonrelativistic limit regime

@article{Lemou2016UniformlyAN,
title={Uniformly accurate numerical schemes for the nonlinear Dirac equation in the nonrelativistic limit regime},
author={M. Lemou and F. M{\'e}hats and X. Zhao},
journal={arXiv: Numerical Analysis},
year={2016}
}
• Published 2016
• Mathematics
• arXiv: Numerical Analysis
• We apply the two-scale formulation approach to propose uniformly accurate (UA) schemes for solving the nonlinear Dirac equation in the nonrelativistic limit regime. The nonlinear Dirac equation involves two small scales $\varepsilon$ and $\varepsilon^2$ with $\varepsilon\to0$ in the nonrelativistic limit regime. The small parameter causes high oscillations in time which brings severe numerical burden for classical numerical methods. We transform our original problem as a two-scale formulation… CONTINUE READING
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