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}
}
  • M. Lemou, F. Méhats, X. Zhao
  • 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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