Low-regularity integrators for nonlinear Dirac equations

Katharina Schratz, Yan Wang, Xiaofei Zhao

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

In this work, we consider the numerical integration of the nonlinear Dirac equation and the Dirac-Poisson system (NDEs) under rough initial data. We propose an ultra low-regularity integrator (ULI) for solving the NDEs which enables optimal first-order time convergence in Hr for solutions in Hr, i.e., without requiring any additional regularity on the solution. In contrast to classical methods, a ULI overcomes the numerical loss of derivatives and is therefore more efficient and accurate for approximating low regular solutions. Convergence theorems and the extension of a ULI to second order are established. Numerical experiments confirm the theoretical results and underline the favourable error behaviour of the new method at low regularity compared to classical integration schemes.

Original languageEnglish
Pages (from-to)189-214
Number of pages26
JournalMathematics of Computation
Volume90
Issue number327
Early online date7 Aug 2020
DOIs
Publication statusPublished - Jan 2021

Keywords

  • Dirac-Poisson system
  • exponential-type integrator
  • low regularity
  • Nonlinear Dirac equation
  • optimal convergence
  • splitting schemes.

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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