Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Low-regularity integrators for nonlinear Dirac equations
HTML articles powered by AMS MathViewer

by Katharina Schratz, Yan Wang and Xiaofei Zhao HTML | PDF
Math. Comp. 90 (2021), 189-214 Request permission


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 $H^r$ for solutions in $H^{r}$, 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.
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC (2010): 35Q41, 65M12, 65M70
  • Retrieve articles in all journals with MSC (2010): 35Q41, 65M12, 65M70
Additional Information
  • Katharina Schratz
  • Affiliation: Heriot-Watt University and LJLL (UMR 7598), Sorbonne Université, UPMC, 4 place Jussieu 75005 Paris, France
  • MR Author ID: 990639
  • Email:
  • Yan Wang
  • Affiliation: School of Mathematics and Statistics, Central China Normal University, 430079 Wuhan, People’s Republic of China
  • Email:
  • Xiaofei Zhao
  • Affiliation: School of Mathematics and Statistics; and Computational Sciences Hubei Key Laboratory, Wuhan University, 430072 Wuhan, People’s Republic of China
  • MR Author ID: 1045425
  • Email:
  • Received by editor(s): June 22, 2019
  • Received by editor(s) in revised form: March 24, 2020
  • Published electronically: August 7, 2020
  • Additional Notes: The first author has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 850941).
    The second author was supported by the Fundamental Research Funds for the Central Universities CCNU19TD010.
    The second author is the corresponding author.
    The third author was partially supported by the Natural Science Foundation of Hubei Province No. 2019CFA007 and the NSFC 11901440.
  • © Copyright 2020 American Mathematical Society
  • Journal: Math. Comp. 90 (2021), 189-214
  • MSC (2010): Primary 35Q41, 65M12, 65M70
  • DOI:
  • MathSciNet review: 4166458