This repository contains information and code to reproduce the results presented in the article

@online{ranocha2025high,
  title={High-order mass- and energy-conserving methods for the
         nonlinear {S}chrödinger equation and its hyperbolization},
  author={Ranocha, Hendrik and Ketcheson, David I},
  year={2025},
  month={10},
  eprint={2510.14335},
  eprinttype={arxiv},
  eprintclass={math.NA}
}

If you find these results useful, please cite the article mentioned above. If you use the implementations provided here, please also cite this repository as

@misc{ranocha2025highRepro,
  title={Reproducibility repository for
         "{H}igh-order mass- and energy-conserving methods for the
         nonlinear {S}chrödinger equation and its hyperbolization"},
  author={Ranocha, Hendrik and Ketcheson, David I},
  year={2025},
  howpublished={\url{https://github.com/ranocha/2025_nls}},
  doi={10.5281/zenodo.17361026}
}

We propose a class of numerical methods for the nonlinear Schrödinger (NLS) equation that conserves mass and energy, is of arbitrarily high-order accuracy in space and time, and requires only the solution of a scalar algebraic equation per time step. We show that some existing spatial discretizations, including the popular Fourier spectral method, are in fact energy-conserving if one considers the appropriate form of the energy density. We develop a new relaxation-type approach for conserving multiple nonlinear functionals that is more efficient and robust for the NLS equation compared to the existing multiple-relaxation approach. The accuracy and efficiency of the new schemes is demonstrated on test problems for both the focusing and defocusing NLS.

To reproduce the numerical experiments presented in this article, you need to install Julia. The numerical experiments presented in this article were performed using Julia v1.10.10.

First, you need to download this repository, e.g., by cloning it with git or by downloading an archive via the GitHub interface. Then, you need to start Julia in the code directory of this repository and follow the instructions described in the README.md file therein.

• Hendrik Ranocha (Johannes Gutenberg University Mainz, Germany)
• David I. Ketcheson (KAUST, Saudi Arabia)

The code in this repository is published under the MIT license, see the LICENSE file.

Everything is provided as is and without warranty. Use at your own risk!