{
  "id": "1804.08575",
  "version": "v1",
  "published": "2018-04-23T17:14:28.000Z",
  "updated": "2018-04-23T17:14:28.000Z",
  "title": "A note on continuous-stage Runge-Kutta methods",
  "authors": [
    "Wensheng Tang"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "We provide a note on continuous-stage Runge-Kutta methods (csRK) for solving initial value problems of first-order ordinary differential equations. Such methods, as an interesting and creative extension of traditional Runge-Kutta (RK) methods, can give us a new perspective on RK discretization and it may enlarge the application of RK approximation theory in modern mathematics and engineering fields. A highlighted advantage of investigation of csRK methods is that we do not need to study the tedious solution of multi-variable nonlinear algebraic equations stemming from order conditions. In this note, we will discuss and promote the recently-developed csRK theory. In particular, we will place emphasis on structure-preserving algorithms including symplectic methods, symmetric methods and energy-preserving methods which play a central role in the field of geometric numerical integration.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-23T17:14:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "continuous-stage runge-kutta methods",
      "nonlinear algebraic equations stemming",
      "first-order ordinary differential equations",
      "rk approximation theory",
      "multi-variable nonlinear algebraic equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}