{
  "id": "1710.03946",
  "version": "v1",
  "published": "2017-10-11T07:42:38.000Z",
  "updated": "2017-10-11T07:42:38.000Z",
  "title": "Dynamics, numerical analysis, and some geometry",
  "authors": [
    "Ludwig Gauckler",
    "Ernst Hairer",
    "Christian Lubich"
  ],
  "comment": "prepared for the Proceedings of ICM 2018 (Christian Lubich's plenary talk)",
  "categories": [
    "math.NA"
  ],
  "abstract": "Geometric aspects play an important role in the construction and analysis of structure-preserving numerical methods for a wide variety of ordinary and partial differential equations. Here we review the development and theory of symplectic integrators for Hamiltonian ordinary and partial differential equations, of dynamical low-rank approximation of time-dependent large matrices and tensors, and its use in numerical integrators for Hamiltonian tensor network approximations in quantum dynamics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-11T07:42:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "numerical analysis",
      "partial differential equations",
      "hamiltonian tensor network approximations",
      "time-dependent large matrices",
      "geometric aspects play"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}