{
  "id": "1110.1120",
  "version": "v2",
  "published": "2011-10-05T23:52:27.000Z",
  "updated": "2017-10-27T21:29:19.000Z",
  "title": "Systematic Discovery of Runge-Kutta Methods through Algebraic Varieties",
  "authors": [
    "Ivan Martino",
    "Giuseppe Nicosia"
  ],
  "comment": "A copy of the software can be obtained by sending an email to the authors",
  "categories": [
    "math.AG",
    "math.CA",
    "math.OC"
  ],
  "abstract": "This work presents a new evolutionary optimization algorithm in theoretical mathematics with important applications in scientific computing. The use of the evolutionary algorithm is justified by the difficulty of the study of the parametrization of an algebraic variety, an important problem in algebraic geometry. We illustrate an application, Evo-Runge-Kutta, in a problem of numerical analysis. Results show the design and the optimization of particular algebraic variety, the explicit s levels Runge-Kutta methods of order q. The mapping between algebraic geometry and evolutionary optimization is direct, and we expect that many open problems will be modelled in the same way.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-10-05T23:52:27.000Z",
      "title": "Evolutionary Optimization for Algebraic Varieties, Design of Robust Runge-Kutta Methods",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2017-10-27T21:29:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14P05",
      "13P15",
      "65L06",
      "68T20"
    ],
    "keywords": [
      "algebraic variety",
      "robust runge-kutta methods",
      "algebraic geometry",
      "evolutionary optimization algorithm",
      "levels runge-kutta methods"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.1120M"
    }
  }
}